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Make sure its clear, as it will leave a hairline mark that you don't want. Use very little on both surfaces, less near the areas from which it can be seen.
There are cyanoacrilates - superglues - specifically designed for gluing wood. Check Lee Valley's or Brownells' offerings. IF a wood repair is done very carefully, it can be close to undetectable. Badly done it can stand out like a sore thumb.
Any glue will work well but the part needs to be clamped exactly in place (heavy rubber bands work well sometimes) with the excess glue forced out of the joint or the repair will be quite noticable. Then bolt handle clearance should be done, and a light sanding with 600 grit wet paper and a bit of stock finish should hide it real well.
If the chip fits nice use some carpenter's glue.
push it together wipe the squeeze out off with a wet cloth
and wrap it with surgical cord if it's hard to clamp.
I used polyurethane (Gorilla type) glue when I laminated up the birch plywood to make the target rifle stock. Clamping is really important if a wide glue line is to be avoided.
Another consideration - worth an experiment - is if the glue used will take a stain if necessary.
I used the "Hot Stuff" cyanoacrylate from CA Glues (bought at Lee Valley Tools) to repair a hairline crack in the wrist of my Marlin 1895. The crack was too small for a thicker glue; Hot Stuff is the consistency of water. (The other CA glues, like Super T, are thicker if more gap-filling is necessary.)
I put a little lacquer thinner in the crack first to deal with any oils, wicking it out with a bit of cloth. The stuff sets up FAST, though, so don't muck about!
I believe epoxies, such as AcraGlass, can be thinned (with acetone??- I'm not sure) but I you have to be careful not to "break the back" of the glue by thinning too much.
Black electrical tape just keeps pulling, great for odd surfaces. Depending on what you're doing a layer of plastic food wrap first keeps the tape glue off or put the tape on upside down since you over lap lots anyways, but it will slide if at an angle. Car wax on the wrap keeps glue from sticking to it.