Removing old gum from a wooden chair...  

Not sure, but. . .
how about heating gently with a hair dryer, then scraping, finally mopping up with mineral spirits ?

Lighter fluid works great for removing
paper labels from wood or paper surfaces, you might try getting some of the lighter fluid. It won't hurt the finish of the wood and it does loosen a lot of things.

.
That's naptha. Might work. This page, on wood floor maintenance, suggests mineral spirits ("paint thinner").
Yahoo "How It Works" suggests hot soapy water. . .! Yeah, right.
http://www.howtocleanstuff.net/floors-and-carpet/floors/how-to-clean-woo...

Freezing spray...
is a great way to remove gum. Freezes it and then chips right off. Never tried it on wood so I don't know if it might harm the wood, but not sure that it....wood.

Peanut butter
and patience.

Pnut butter
reminds me of a bad experience with chewing gum and hair when I was a kid. I think I tried peanut butter, then finally cut it out in desparation. 🙁

Thanks all
For the suggestions. I think I will leave the gum for now until I summon the courage to try one of these methods.

So it is under the seat?
Some gum chewers are so classy.
It sticks really well on wood that is less finished. No barrier between the gum
and the wood fibers.
Holding an ice cube on it (ice in a zip-lock) for a few minutes should make it
a much harder mass than the wood. It may pop right off with a little help from
screw driver tapped with a hammer.

Yes
The gum is under the seat... of a Grand Prix, no less.
Tres classe 😮