If you walk towards a chest and jump just as you are about to hit it, there is a slight chance that you clip straight through the chest and find yourself inside it. You can then jump to enter nearby chests. The attached video describes the glitch better than I can, so I suggest watching it.
Environment
Minecraft 1.4.7, tested several times. Failed to reproduce the glitch several times; had to record four times.
Apple Macbook pro, Mac OS X 10.7.5, Java 1.6.0_37, 64-bit (although minecraft only recognizes it as 32-bit)
Duplicate of MC-1635 , please use the search function to see if your bug has already been submitted. Currently over 45% of tickets are being closed as duplicate.