You need to use shims. Clean the hole in the chair leg of old glue. Before applying more glue, insert the rung to the hole with enough shims to create a snug fit. Then remove the rung and shims, apply fresh glue and reinsert the rung and shims to the hole at the same time. You may need to use a small tool to push the shims so they don't extend beyond the hole opening. Apply clamping straps to hold, clean away any excess glue and allow the glue to dry for the prescribed amount of time. This should create a tight fit.
You can buy shims at hardware and woodworking stores.
Paula R.
June 2007