Jim-
You don't say whether or not you have a windlass.....
1. If you don't have a windlass, use a metal stainless (best) or galvanized thimble around the chain's last link, wrapping the three strands around it and then braiding them back into the rope. This is the strongest and most chafe free set up, but won't pass through a windlass, and can also be difficult to pass through a small deck pipe in larger diameters of ropes and chains on big boats.
2. If you have a windlass, try the standard method where all three strands are passed around the last link of the chain and then braided back into the rope, being tapered after the first few tucks. This is a proven, workable method. If your windlass will pass this type of union, you're home free.
These first two methods are discussed
HERE.
3. If method 2 produces an enlarged diameter union that jams when going through your particular windlass, we need to go to method three, where we weave the strands down into the chain, or at least some of them, in order to further reduce the union's diameter. I discussed my variation in the thread linked above by my good friend Harvey, and of which another variation is described
HERE.
My method varies from the one discussed above in how the third strand is treated, mine going back into the rope instead of down into the chain, and also in that the two that go down into the chain are sewn together repetitively each time they pass each other on their way down the chain, which insures further that they won't slip out backward. This may be a bit of overkill, but it's in my game plan, and I'm sticking with it for the time being for safety's sake.
I developed my method on my own, independently. I first thought about weaving all three down into the chain, but decided to do that with just two, as it was easier and simpler to do, and to take the third backward into the rope. This makes for a smaller diameter splice, which I needed for my windlass, and just seemed more logical and easier to do.
Dr. Bob Austin did a single test of this method, and found it worked well, but did not do a heavily loaded test on it repetitively to the failure point or make comparisons to other methods for comparisons.
I've never had any trouble with mine.
Lots of possibilities to consider here!
Would love to have the equipment and time to test all these ideas out against each other!
Joe. :teeth :thup