Hash table

Is it ever possible to have a Hash table that can do get,put,remove @ O(1) for Strings?

calculating the hash for the String alone is O(n), is it not? [that's if you want to produce a good hash that won't collide all over the place]

It's easy on a Turing machine, just use the infinitely long strings as indices into the infinite memory and keep the entries infinitely apart so any string can be stored.