Personal choice by the performer. But chair for chairman/woman sounds odd to me. It sounds like a piece of furniture. It is unfortunate that women regard themselves as so inferior to men that the word chairwoman is thought undesirable. The same applies to actress. One old judge used to tell juries to appoint a foreman, saying that the foreman could, of course, be a woman, but "When I have duck served at dinner, I do not enquire whether it is a duck or a drake".
(And the Bench sounds like furniture too, but that's a little different from 'chair' !)