I'v been running one of my freezer chests off a cheap ebay PID for two years now. It works great. At first I tried to use a SSR and the PID, but the rapid cycling of the PID would not allow the compressor to turn on. The one I got has a 10A relay for the high temp alarm, so I wired the power supply for the compressor through the high temp alarm. No SSR needed.
from looking at the manual runningweird posted the alarm on this PID is rated at 1A for 250VAC (or is it 3A?) , so this PID might not work too well to run the compressor off the high temp alarm.
Personally it was more hassle than it was worth, and setting the temp is some what of a chore. I'd go with a $50 ranco controller . Ive bought 4 from these guys over the years.