One of the simpler ways of splicing rope to chain is to seize the rope about 16 inches in from the end to arrest any further unravelling. Use ordinary whipping twine.
Unlay the twist to the seized point. Taping the ends with electrical tape just makes it easier to splice later on.
The next step is to feed 2 strands through heat shrink in one direction and one in the opposite direction. Pull all the strands tight and apply heat to shrink. Preferably a high heat hair dryer.
Cut the whipping carefully. Anyone who has done an eyesplice with 3 strand twist will be able to do the rest. Over one and under the next in a typical backsplice fashion.
After 3 complete tucks reduce the tails by 1/3rd and with a hot knife melt flat Continue with the tucks for about 3 more with each tail and this will give you a nice taper. Cut off remaining lengths and melt flat.
Finished product should look like picture above.
For a simple way to splice Chain and Rope just follow the six steps listed below: