File:The Hop Pole, Beeston - Chilwell - Geograph.org.uk - 660204.jpg
This leads to the tail that in the past, when each of these settlements were under different local government (they are now both in The Borough of Broxtowe) there was a different closing time in the two areas. As a result there was a nightly migration from one side of the bar to the other when one half of the establishment had to stop serving.
Whether there is any truth in this story I have no idea. It would have had to have happened before 1934, which is when Stapleford Rural District (containing Chilwell) was merged with Beeston Urban District to become Beeston & Stapleford Urban District - eliminating this border.
Unfortunately I was unable to get a satisfactory close-up of the sign due to a strategically placed parking sign.(required by the license)