How to repair hole that the chair leg screws into

1. Fill the hole with elmers or other wood glue.
2. Fill the hole with a mixture of glue and sawdust or flour.
3. Fill the hole with glue and jam a golf tee in it (saw off end of golf tee after its dry.
4. Fill the hole with wood putty available at big box stores.

Then, depending on your skill, energy, etc.:

1. Get a double ended screw from big box store
2. Drill pilot holes and screw your leg back in
3. Put the leg in while the glue is drying and use clamps or tape or just balance it while the glue sets.

Repair it using the same hardware it originally had. It sounds like the chair had a T-Nut inserted:

Assuming the "male" screw in the leg still has good threads (you did not indicate that it was bad), buy a matching T-Nut at a good hardware store.

Note- there are quite a few sizes and types of T-Nuts, bring a sample from one of the other legs/chairs.

What I did was peeled back (removed staples) a corner of the liner underneath the chair and closest to the leg. I reached up in there above the diagonal wood brace that the leg is screwed into. I could feel what I think was the t-nut above the brace. It was loose and not seated in the brace anymore. I couldn't reseat it (can't get a hammer in there and no clearance to be able to hammer it back in) but at least I could hold it down and keep it from turning while I screwed the leg into the t-nut. That worked for me. Easy peasy.