though dormant pruning is much more common, I almost exclusively summer prune. dormant pruning stimulates rank regrowth the following season, which I generally try to avoid, as it usually makes more pruning necessary.
summer pruning, on the other hand, decreases vigor somewhat, which is what I'm after when pruning established trees. this is especially true for fruit trees on dwarfing
root stock that are getting a bit too big. summer pruning can cause sunburning if done when the sun is too intense or if too much is removed.
I think thinning some lower branches on a chestnut would likely be just fine this time of year, depending (of course) on
local conditions, the age of the tree, and your goals.