This is how I keep my necklace chains from tangling. It's extremely effective, space-efficient, and cheap.
Step 1: Gather Your Materials
You'll need a pair of scissors and some thin cardboard.
Step 2: Cut the Spools
Cut small rectangles out of the cardboard, about 4.5x3 centimeters.
Carefully cut out approximately 3x.5-1 centimeters along the middle of the long side.
Step 3: Wrap the Chain
Start wrapping the chain around the spool. Leave just enough of the ends loose (see the picture) that you can clasp them together.
If you're worried about the ends being too loose (and therefore at risk of falling off the spool), just shake the spool a bit and the chain will distribute itself more evenly, or take the chain off and cut into the spool a little more deeply.
Step 4: You're Finished! Also...
Once you're done putting your chains on cardboard, you can save other things from the dreadful fate of entanglement with cardboard spools of various sizes, including string and beaded holiday garlands.