I've never seen a chine added on to the exterior of a hull. It would seem like way more work to make it separately and bond it on. Not saying it isn't possible, just that I've never seen it. You might want to investigate furter- look inside the bilge at the bottom contour.
Having said that, if it is a hollow cavity...
There are injectable, grout-filled epoxies available. I use one that I've posted about before. It costs about $1.50 an ounce which is a little less than a cubic inch. It would cost mucho dinero to do what you're considering.
There are rigid foams available- you'd need to find one that was closed-cell so it wouldn't fill with water. They would give you a little bit more support but nowhere near what the first solution would provide. Would have a fraction of the cost though.
I suppose you could stand the boat on its nose and pour the cavity full of resin. Without some sort of reinforcement, it will have more support but probably not more strength.
Consider this though- most boats perform fairly well in their intended purpose. If you're running hard, wave jumping, etc., the hull might not be up to what you're asking it to do. Throwing more money and effort into it may be futile. You'll just move the likely failure point to the next spot down the chain. If you want to run hard, maybe you boat is telling you it's time to move up- while there's still some value left in your existing boat. If you bust the hull, it's not going to go too far as the down payment on the next one.