How to generate a list of random numbers between -1 and 1 with sum 0 in Julia?

I'm currently working on implementing a simple genetic algorithm in Julia, and I need a way to generate n random numbers between -1 and 1 with a sum of 0. Ideally, the distribution would be uniformly random, but it would still work as long as it's a reasonable approximation. A search on Google returns these two posts (1, 2) which were related but not exactly what I'm looking for.

I've reduced the problem to generating n numbers in the range [0, 1] with sum n/2, but I'm not sure where to go from there.