I solved this problem this evening. The tension can be tremendous, and you're pulling against it. It goes as 1/sin(a), where a is the little angle of an almost tight chain. You know how tangent goes to infinity, so does the tension.
This requires some rope, 15 feet and two 2 feet lengths. An old coat hanger with pretty thick wire. And a wood clamp: the kind that's 18" or 24" long and is closed by squeezing a trigger/handle.
The idea is to relax the chain, set the chain on the sprocket, and tighten the chain.
So, going down the length of the chain and wire, I tied 3 or 4 loops, with the 15 foot clothes line, around the chain and wire to hold them up against pole. There was enough slack for the chain to pull through the loops. This relives much of the tension.
I made two hooks out of thick coat hanger wire. Each hook had one end bent to go through a chain link, and, on the other end, a larger hook to tie onto the 2 foot rope. (I think a loop of coat hanger wire is a bit stronger and more secure.) The idea is to relax the chain, set the chain on the sprocket, and tighten the chain.
I made loops out of the 2 foot ropes. Each loop went around different arms of the wood clamp.
Each loop hooked through one of the coat hanger hooks.
One hook (smaller hook end) went through the eye of the wire cable, where it attaches to the chain release mechanism. The other hook went through the chain. When the wood clamp is closed, the hooks are about 15" apart, and the mechanism of hook, rope, wood clamp, rope, hook, has taken up the tension and put slack at the tensioning bolt. (I put in a keeper rope between the two loops just in case the wood clamp let go.)
Remove the tensioning nut, and back the other nut up toward the chain.
Now release the wood clamp 12" to 14". (At this point, I put a loop of chord around the bar and clamp to bear the weight of the wood clamp.) The chain is going to have about a foot of slack. If this isn't enough slack, you can release the wood clamp further.
Go to the garage door opener, and put the chain on the sprocket. Save yourself some trouble and make sure the chain is going through the plastic chain guide.
Tighten the wood clamp. Put the nut back on, and take advantage of the chain slackness to finger tighten the nut.
You still have to tighten the chain, and readjust the garage door opener limits. (Those racheting box wrenches are wonderful for tightening the nut.)
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