Can I have a fire in my fireplace while the central heat is on?

Sure.

The extra heat is also likely to keep your central heat from having to kick on as often (unless you have a really poorly designed fireplace that produces negative heat gain by sucking the warm air from your house up the chimney, but this is pretty unlikely)

Yes, I have both going right now. It’s a good way to cut down on your heating bill.

You may wish to crack open a window in the room with the fireplace just until the fire catches enough to heat the chimney. Otherwise, depending on how airtight your home is, the smoke may draw into the house instead of out the chimney.

@angiesquestion What were you concerned about?

we do it all the time. The only concern I could envision is the central heat causing a positive pressure in that room making the fireplace become unruly. But that would have to be an over awesome air delivery system to even figure in that way.

Yes, Westcoasters do it all the time.