Can a rusty chain be saved? I picked a girl's mountain bike out of a dumpster . It looks very excellent except for a chain that is so rusted that each link needs to worked free.

Name is Techno Lite , 26" wheels, 15 speed Shimano, center pull brakes Lee Chi. 

I know it is not the caliber of bike that most posters here have, but I have a 11 year old granddaughter that could ride it ; a "starter" bicycle to see if it is something she would be interested in. My guess is some one rode on a salt water beach then put it in a garage for years without rinsing it; the chain was essentially solid.

Question: Should I oil the chain and work it free or buy a new chain ?
If the chain isn't worn (which it probably is not, kids bikes don't get high mileage) it might be worth trying to save, but you may end up spending more compared to getting a new one.

Penetrating oil, a wire brush and a lot of effort may free it up enough and get it reasonably clean.

Removing the rust chemically is problematic. Something strong enough to work with the chain in place may damage paint or plastics. There are safe products such as Vapo-Rust but the chain would need to be removed and soaked for an extended period of time. Also, new chains for 10 or 15 speed bikes are inexpensive. Instead of buying chemicals, just buy a chain.