Hard to tell w/o hearing the clicking, but your description certainly sounds like it could be a bad lifter --- clicks until enough oil pressure has built up and the noise goes away.
You might want to get a second opinion from another mechanic. I
The chain itself is not neccesarily the main issue for concern, but the upper chain guide rails. They are made of plastic and become brittle over time. Since you don't know the oil change history, wouldn't be a bad idea to pull the valve covers and inspect them.