You could use a database instead -- PostgreSQL has some special indexing capabilities optimized for this type of data which is located by X and Y coordinates. You can also specify that the data returned is within a certain radius rather than in a square or oblong shaped area.
PostgreSQL (free and open source)
There are other databases as well, and for the client-side you may find certain types to be better-suited to this since they can run stand-alone (initiated by your game client application) or can be included as part of a code library that you can "just use." The advantage is that you don't have to design an indexing scheme because most SQL database engines already do this quite well.
An advantage with the database approach is that you can make your chunks smaller (or get rid of chunks completely and just use tiles directly, but the use of at least small chunks/groups of many tiles may be more efficient depending on your design), and then use the SQL query to bring in a larger area than is viewable. By pre-loading to overlap nearby non-viewable areas, the tiles can be prepared before the player moves their character, resulting in a better (hopefully smoother) gaming experience.
I've noticed that some games keep a "cache" of the map data on the local hard drive after obtaining it the first time (this is undoubtedly to reduce network I/O), such as Ashen Empires:
Ashen Empires (free to play, beautiful 2D implementation)
Keeping track of "last updated" timestamps with each chunk/tile will also be helpful since, for where locally stored data is available, the SQL query could include an additional "WHERE timestamp_column > $local_timestamp" clause so that only updated chunks/tiles get downloaded (two benefits of saving bandwidth like this are lower connectivity costs, and less lag for your players, which will become more obvious when your game gets popular).
A screen shot from Ashen Empires (a few characters are at a local bank, and by the looks of those bones on the floor it looks like a few skeleton monsters must've wandered in and were likely slaughtered by the local town's guards):