Yes, just remove the hull and eat the nut raw. A good way to do that is split in half with a knife, and that makes it easier to get out.
They develop a much better, sweet taste if you let them just sit for a few days. Much of the moisture leaves the nut and it shrinks. You can tell when this happens by pushing on the outside with your thumb. When the hull sinks in a little, they are ready to eat. However, if you leave them too long they will get too hard and dry and not be as good.
They are fine to eat a little green, but I doubt you will like the taste. There is no bitterness, but it is just kind of a bland taste. But when that sweetness develops after a few days, its like eating an entirely different nut.
A little experimenting is all it takes, and you soon get the hang of it. I'm 61 and been eating chestnuts since I was 7 years old. I have it down pretty pat.