I like hunter green, lime green and white with some sparkle like rhinestones and gold lamay. Add some beige chaps or pants. Or how about teal blue, with silver and some chocolate brown somewhere.
Purple! What? No, purple doesn't really work. I'd never put pink on any horse regardless of the colour. Red looks awful on chestnuts.
Navy blue works well, so do most shades of green. White always looks good. Can't go wrong with black! Light blue and navy together look really good. And, as part of my Pony Club's old uniform, we used to have these checked saddlecloths with a gold trim. The check had a bit of brown, dark green, dark gold/whisky in it. I looks really good on my chestnut.
Actually, I agree with the purple idea. It sounds awful, but it does work with chestnut, and with most other colours as well. It seems to be a neutral for horses.
I like navy blue best, and dark green. Browns and tans always work with chestnut, regardless of the shade. We have two very bright (new copper penny) chestnuts, and they (and we) wear black, white, or navy with them. We have bays and a grey as well, so black, white, and navy work for them as well. Red is a total disaster for chestnuts, and yellow just makes them look yellow, so I stay far away from both of those.