Making wood lighter isn't easy. Some hardwoods can be bleached, but it always requires stripping. It's always easier to make wood darker than lighter. Chestnut is one of the hardwoods, but I've never had an opportunity to use a bleach on it. I've used bleach on oak and on maple and both handle it well. Softwoods like pine and fir are heavily damaged by bleaching.
So I guess the answer is that there is no easy way to get what you want. If you decide to try stripping and bleaching, I'd suggest that you start by buying a small piece of chestnut and appy household chlorine bleach to it, keeping it wet with the bleach for a couple of hours. If the wood come out looking "furry" when it's dry, then bleaching isn't an option and the only way to make it lighter is to sand the wood down past the stain.