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I would not recommend this! Games are games and GUIs are GUIs. Just because they're not console applications does not mean that they're equivalent. I'd HIGHLY recommend something like the Lightweight Java Game Library (LWJGL) http://www.lwjgl.org/ You may not have many problems with Swing (though I think of many off the bat) but if you want to learn how to ...
Swing should be fine for your needs. You should check out this stackexchange for other possible problems with Swing.
Maybe you should consider making a two dimensional array for the chunks,  being the top left chunk of the map. That way you always know which chunks are surrounding the player and if the player reaches an end, you can put the first chunks next to the last ones, if you want to make the map loop.
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