Yes you can convert your wood burning fireplace. The most energy efficient way to do this conversion is with a gas insert, which is basically a gas fireplace
that fits into your old wood fireplace.
These days the inserts are direct vent and sealed combustion, which means they not only exhaust to the outside, but all the air required for combustion is also coming from outside. This is most beneficial as the fireplace is not drawing in room air for combustion, when installed correctly there is little to no heat loss, and they have excellent efficiency ratings some as high as 82% AFUE (annual fuel usage efficiency). Also, the gas inserts are available in a variety of sizes so they can fit virtually every wood burning firebox, even zero clearance boxes.