Denis Hassabis was asked this in a Q&A after a talk he gave and according to him someone did this (bootstrap a chess engine from self play) successfully, while still being a student and was hired by them subsequently.
I didn't see the talk, but I'm guessing he was referring to the Giraffe engine done by Matthew Lai (https://arxiv.org/abs/1509.01549). The main thing there is that he only learns an evaluation function, not a policy. Giraffe still uses classical alpha-beta search over the full action space. AFAIK nobody has learned a decent policy network for chess, probably because 1) it's super tactical, and 2) nobody cares that much because alpha-beta is so strong
