Greetings wesbrew - I have a plate chiller by Blichman and it's quite stable no matter which if it's sides I set it on. So I would tend to agree with Tuna and suggest it has a mfg defect. I would send it back unless you're happy with paying for a product that was made wrong. If so, I would test it as Tuna suggested.
I would close one end of the water side, pump it full of air at maybe 50 PSI and submerge the chiller in a bucket of water. If you leave the wort ports open and air comes out, you know you have an internal leak. Then reverse the process and test the wort side, but I would only pump it up to 5-10 PSI.