The rescue of Roger Mallinson and Roger Chapman occurred between 29 August and 1 September 1973 after their Vickers Oceanics small submersible Pisces III was trapped on the seabed at a depth of 1,575 feet (480 m), 150 miles (240 km) off Ireland in the Celtic Sea. The 76-hour multinational rescue effort resulted in the deepest successful submarine rescue in history.

The Canadian commercial submersible Pisces III measured 20 ft (6 m) long by 7 ft (2 m) wide by 11 ft (3 m) high. It was built by International Hydrodynamics of North Vancouver, British Columbia, and had been launched in 1969. Pisces III originally had tail fins, which were removed to improve access and handling when the submersible was purchased by Vickers Oceanics. Had the fins been retained, they would have prevented the entanglement of the towline on the craft's machinery sphere which caused the 1973 accident.

Pisces III had sunk once before, during trials in Vancouver Bay in 1971. Peter Messervy of Vickers Oceanics, who would lead the rescue team after the 1973 accident, was one of the pilots who was rescued by the Canadian Defence Ministry submersible SDL-1.

The Pisces III submersible was crewed by 28-year-old pilot Roger Chapman, a former Royal Navy submariner, and 35-year-old engineer and senior pilot Roger Mallinson. Chapman had been invalided out of the Royal Navy due to less-than-perfect eyesight.

During the early hours of Wednesday, 29 August 1973, Chapman and Mallinson began a routine dive, Dive 325 of the Pisces III. They were working on laying transatlantic telephone cable on the seabed, approximately 150 mi (130 nmi; 240 km) southwest of Cork in southern Ireland. Their job entailed an eight-hour shift in the six-foot (1.8 m) diameter submersible, which moved along the seabed using water jets to liquefy the mud and lay cable, then cover over the cables. The submersible would usually take approximately 40 minutes to reach a depth of 1,600 ft (488 m).

For Mallinson, this dive was additionally fatiguing, as he had spent over a day previously repairing a broken manipulator on the submarine. During the repair he changed the oxygen tank for a full one. During each dive the pilots had to ensure that after every 40 minutes they turned on a lithium hydroxide fan to remove carbon dioxide from the atmosphere and also add additional oxygen. Additionally, they maintained a video commentary record during every dive.

Shortly after 9 a.m., with the submersible about to be lifted out of the water with a towline back onto the ship, a water alarm sounded in the aft sphere, a self-contained part of the submersible containing machinery and oil storage. The towline had apparently fouled on the aft sphere hatch and wrenched it open. The crew heard the sound of water entering the aft compartment as Pisces III became inverted and began to sink back to the seabed. The aft sphere was fully flooded with over a tonne of water.

At 175 ft (53 m) the submersible jolted to a stop – held at the maximum length of the nylon towline. The crew swung about in the sea currents until the rope snapped. The pilots immediately closed down all the electrical systems which left the sub in total blackness. They also managed to release a 400 lb (181 kg) lead ballast weight as they descended. They impacted the sea floor at 9:30 a.m., at a speed later judged to be at 40 mph (18 m/s; 64 km/h).

Using a flashlight, the crew was able to review their surroundings and also called their mother ship to update them. The full tank of oxygen Mallinson had added had a capacity to last approximately 72 hours, but eight hours had already been used, leaving 64 hours.

Mallinson and Chapman spent the first few hours sorting out the submersible which was almost upside down. They checked all the watertight doors for leaks and prepared for rescue to come. To preserve oxygen they knew they had to make as little physical exertion as possible, not even speaking. They made themselves as comfortable as possible as high up as they could get to avoid the foul air that sank down.

The pilots had just a single sandwich and one can of lemonade on board. They also decided to allow the carbon dioxide in the air to build up beyond the normal 40 minutes to conserve oxygen, which resulted in lethargy and drowsiness for both men.

At 10:35 a.m., the support ship Vickers Venturer, then in the North Sea, was ordered to return to the nearest port with the submersible Pisces II aboard (which could be removed and flown to Ireland). Additionally, at midday the Royal Navy survey vessel HMS Hecate steamed to the accident location to offer assistance with special ropes. The United States Navy offered a submersible belonging to the U.S. Salvage Department, called a Controlled Underwater Recovery Vehicle (CURV-III), which was sent from California, and the Canadian Coast Guard ship John Cabot left from Swansea.

On Thursday 30 August the Vickers Voyager arrived in Cork at 8:15 p.m. and loaded the submersibles Pisces II and Pisces V, which had been flown in overnight. The ship left Cork at 10:30 p.m.

At 2 a.m. on Friday 31 August the Vickers Voyager reached the scene and launched Pisces II with a polypropylene rope attached. However, the lifting rope broke free of the manipulator arm and the submersible had to return to the surface for repairs. An attempt made by Pisces V failed to find the crashed Pisces III and returned to the surface after it ran out of power. The relaunched Pisces V had more success and found the crew at 12:44 p.m. However, an attempt to attach a rope failed. Pisces V now remained with the stricken Pisces III. An attempt to send Pisces II down again had to be called off when it suffered a leak.

Even the newly arrived CURV-III aboard the John Cabot was unable to launch due to an electrical fault. Just after midnight Pisces V was ordered to the surface, leaving the men on Pisces III once again alone. They were running out of both oxygen and the lithium hydroxide to scrub the carbon dioxide from the deteriorating atmosphere in the submersible. Both men were cold and wet and suffering from severe headaches.

The rescue operation of Pisces III commenced early on Saturday, 1 September. The rescue submersible Pisces II was deployed at 4:02 a.m., and within a little over an hour, by 5:05 a.m., it had successfully attached a purpose-built toggle and polypropylene tow rope to the rear sphere of the distressed Pisces III.

The CURV-III, a remotely operated underwater vehicle, also joined the operation. At 10:35 a.m., it managed to fasten another tow rope to the stranded submersible. At this point, the crew of Pisces III consumed their only available food and drink on board.

The lifting of Pisces III began at 10:50 a.m. This procedure caused the submersible to jolt significantly, further disorienting the crew. The lift was temporarily halted at a depth of 350 ft (107 m) to disentangle the CURV-III. At 100 ft (30 m), the lifting process was paused again to allow divers to attach heavier lifting cables to the submersible.

At 1:17 p.m., Pisces III finally broke through the surface. Divers immediately attempted to open the hatch to allow fresh air into the submersible. However, it took nearly 30 additional minutes to achieve this. When the hatch finally opened, both crew members struggled to leave the craft, having been confined inside for a total of 84 hours and 30 minutes. Subsequent evaluations revealed that a mere 12 minutes of oxygen supply remained in Pisces III. Reflecting on the close call, author R. Frank Busby later stated, "... the crew of PISCES III can be thankful they were not 250 miles, rather than 150 miles from Cork."

In 1975, Chapman published an account of his rescue in his book titled No Time on Our Side.

No Time on Our Side, adapted from Roger Chapman's book for Radio Four by James Follett was first broadcast on 2 June 1976. In addition, "Mayday for Pisces III", an episode of BBC One's series Life at Stake was shown on 24 February 1978.

In August 2013, it was announced that a film depicting the events of the rescue was in development, possibly starring Jude Law and Ewan McGregor. In July 2021, Mark Gordon Pictures acquired the rights to adapt Stephen McGinty's book based on the rescue, The Dive, into a film.

• LR5 – rescue submersible designed by Roger Chapman
• Titan submersible implosion

• Busby, R. Frank (1976). Manned Submersibles. Washington: Office of the Oceanographer of the Navy. OCLC 2206798.
• Chapman, Roger (1975). No Time on Our Side. Sidney, B.C.: Gray's Pub. ISBN 9780888260598. LCCN 75-19154. OCLC 15758413.

• McGinty, Stephen (2021). The Dive: The Untold Story of the World's Deepest Submarine Rescue. New York: Pegasus Books. ISBN 978-1-64313-746-9. OCLC 1202305663.