Is it possible to use a 8 pin micro pic to pulse a ground signal? I am trying to use the chip to connect a ground for 2 seconds then no ground for 1 second then back on until power is removed from the chip.

 

Yes.
But you can do the same thing with an LM555 chip.
Many ways to skin the cat.

 

A relay would help, and given the long time intervals (1 and 2 seconds) it would be plenty fast.