Gas fireplace chimneys should be inspected and cleaned annually. There will not be any soot or creosote in the chimney since you are not burning wood, but you may find bird nests that need to be removed.
Carbon Monoxide Is an Issue
Gas fireplace chimneys need to remain open so that carbon monoxide can escape. With wood-burnign fireplaces, you know quickly if the chimney is not open because of smoke in the house. Gas fireplaces, however, produce carbon monoxide, which you cannot see or smell.
Have your gas fireplace chimney inspected and cleaned annually at a minimum, states Fireplaces, and open the flue using a clamp to keep it open. Make sure that carbon monoxide detectors are kept in working order. These measures are necessary to prevent carbon monoxide from building up inside the house.