Excessive Oil Consumption, Low oil pressure at cold start

[tarheel185]

I have a 2005 Tahoe with a 5.3L. Lately in the morning when I start it, the oil pressure gauge sits at zero for a couple seconds (clicking noise form engine), I get the low engine oil pressure warning, and then the needle bounces up to normal, the warning goes away, and the clicking stops. In addition, I have had to add three quarts of oil since the last oil change, mainly after any highway driving. I haven't found a leak so I assume it is burning (but I don't see smoke either). Also, I do not have the same issue for the rest of the day after the first cold start.

My theory is that something in preventing the oil from circulating properly which is causing it to heat up and burn while the engine is running. Has anyone seen this before?

Thanks