Oil leak

Hows everybody doing? I've owned a 2006 silverado extended cab, 5.3, 4x4, for about a month and a half. Probably have put around 300 miles. The other day i hooked up a 5ft x 8ft trailer and i noticed oil droplets on the trailer but the thing is that when the truck is just parked ive never seen a oil leak. Is it possible for a truck to just be leaking while its running and if so where could the leak be coming from?