Is it worth it to strip paint off Cherner chairs?  

Use a chemical stripper,...
Use a chemical stripper, followed by some sanding.
Looks like a good amount of messy work.
Why did they paint them? They were probably beat up and they painted them to update and cover up the wear and tear.
I'm not a fan of these chairs in the first place, but they dont look bad in white.

Get some professional advice!
and don't touch the stripper..and especially the sandpaper until you have better advice.
As always,

Maybe Repainting them
Maybe Repainting them will be a more realistic task. I'd hate to strip them and realize they're not in great shape.
What about dipping them? I've been told some people still
do that.

Youre not going to get much...
Youre not going to get much different advice from a "professional"
Your only options are to chemical strip yourself, have a pro chemically dip strip them (will be pricey) or simply give them a very light sand and repaint them white.

Good Lord....
.

Paint could be original?
They are not Cherner chairs.

Woodywood
Can you elaborate please? I'm not sure what you mean.

The other chairs like this...
The other chairs like this that one sees online, with the much wider "waist" section than Cherner chairs have, also tend to be white.
There was a set at the url below, on 1stdibs, with a Plycraft decal from 1985, calling them the "Rockwell II" chair, designed by Lou App.
http://www.1stdibs.com/furniture_item_detail.php?id=528951

tchp
Thanks. That hits the nail right on the head.