"Walt" wrote

I thought car rental companies frowned on the use of chains,

Yes they do. They also frown on driving on unpaved (dirt) roads.
What they don't know won't hurt them. But you could be in trouble if
they find out.

This is quite strange, chains/cables are, among other things, a safety
device. I'd imagine rental companies will get suied in a blink of an eye
if they prohibit chain installation..

apparently real made-out-of-real-chain chains don't fit in the
wheel-wells of modern cars.

I think it depends on the car.

A lot of expensive cars, esp. with sport package/big wheels don't
have enough clearence for chains. But cheaper ones that are
the bulk of what rental companies offer should not be a problem.