How can I enable Mountain Lion Spellcheck in Google Chrome?
Spell check is a system service so by using the standard Mac control for a text box, chrome would magically get to use the service. 

Since chrome isn't programmed to use the standard control (they wrote their own implementation) - you would need to either get the chrome devs to change the code or you would need to change it yourself and re-compile your version of Chrome. Both are likely to involve a serious amount of engineering since the code base is quite complex.