Chrome on iOS is basically a wrapper around Safari, because Apple don't allow different browser engines on iOS (and how they get away with that I don't know). Currently I think Chrome on iOS uses UIWebView which does not support Javascript JIT compilation (i.e. fast javascript), but I guess Chrome on iOS will soon move to WKWebView which does, so that should significantly improve performance for anything JS-based.
Note that whether or not "asm.js is supported" depends on your definition - technically it is supported everywhere, even on old browsers, because it's just JS code. Whether or not it runs as fast as possible depends on the JS engine optimisations, and that is again different to having a specific parser for asm.js like Firefox has. Safari has a pretty sophisticated JS engine so when it can use JIT asm.js code should be very fast.