Gas exhaust contains nitric acid, which attacks chimney mortar joints and can cause the chimney structure to collapse. All chimneys venting gas exhaust need a properly sized liner, to provide adequate updraft and keep the acid from contact with the mortar.
You also need to have examined, cleaned, and reset the burner & pilot orifices and air intake settings on the appliance, and inspect the gas inlet, connector pipe and flue for gas and exhaust leaks, because system components and fittings deteriorate over time.
The reason for concern is that a leaking, blocked or partially blocked gas flue will usually result in odorless exhaust gases entering the breathing space in the house below. Gas exhaust contains, among other things, carbon monoxide and carbon dioxide. Exposure to these CO gases has recently become a matter of much concern. To read about a recent study regarding long-term effects of exposure to CO, click here