If you are absolutely certain your search string can be normalized (e.g.: stripping all the extra spaces, forcing lower case etc.) so to avoid ambiguity and that you need to search for full match (i.e. you either find exactly the normalized string or not, and don't need to search by substring, soundex, partial match, sort by it etc. - this is how I read your "by exactly this string" ) you could consider calculating the hashcode of the string, put it in the DB and indexing that.
If you use an hashcode function that returns a number, you will have a very efficient access index. And of course you can still keep the original string field for printing and different access approaches.
Possible problems: while hashcode can minimize the chance of a hash collision, they cannot be guaranteed not to happen, so you should manage that, too.
Also, unless you have lots and lots of addresses, I doubt that the speedup gain will be worth the trouble.