I had a Little Chief too, but my first was an antique refrigerator. We're talking 1970's.
It had been dumped on a job site and was missing the door.
The smaller compressor compartment, on the bottom, was separate, so I had to make a hole to the upper part. Then I made a wooden door, used a hole saw to make two exists for the smoke, and a couple of swivel tin can lids to regulate.
A hot plate on the bottom, a pan of wood chips, and I was good to go.
I smoked cured bacon, cured hams, fish, and jerky in it.
There was no plastic anywhere. One time I checked the insulation, is was a few layers of foil on wooden frames, kind of like a canvas paintings.
Wish I had taken a picture of it.
Does a Weber kettle with a fire brick (actually a $4 brickwall cap) count??