The "rising chimp" problem

The new book, Einstein's Puzzle Universe, by Tim Dedopulos, is a compendium of good physics and logic problems. Here's one for you to solve:

Imagine that there is an even rope of negligible weight draped over a wheel, which permits it to slide perfectly freely. Equal lengths of the rope descend from either side. On the left side, the rope ends in a 10 kg weight. On the other side, perfectly level with the weight, is a young chimp, also weighing 10 kg.

When you give a signal, the chimp will start climbing the rope. Which of the two, the chimp or the weight, will reach the top first?

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