Here's the method NE Ropes suggests.
Similar to the one I learned, the Shackle Splice or Crown Splice described in Brion Toss's Chapman's book of Knots. Talking with Brion at a boat show
, I learned some tips to add to his book's description:
1. When you unlay the three strands, and taper and tape their ends, it's good to flatten out each of the three strands, rather than leaving them spiral-wound and round. Flatter strands seem to lay together tighter as your build the splice, and make a fairer and more secure end result.
2. After each round of three tucks, roll the tucked portion in your hands and snug up.
Try this a few times and you'll get the hang of it.
I find the easiest way to set up to do this is to hang the end of the chain in front of you at hand height when you are sitting.
I'd also suggest his splicing tool, the Point Hudson