How do you move chests in your house?

To pick up a chest, it must be empty (otherwise you'd have a "nesting doll" situation that gave you extra inventory space). You can move a non-empty chest without picking it up, however - walk up to the chest with nothing in your hands, and click repeatedly or click and hold on the chest. It will shake for a moment, and then jump one square away from you. If the chest would move into a wall, it will jump to the square behind you instead. This trick is very useful for making minor rearrangements without having to shuffle around lots of inventory items.