Yes, various solutions can be deivsed for living spaces without a chimney.
For example, take an electric hearth. All you need for this is a wall socket. But solutions can always be devised for the placement of a gas-fired hearth or heater. The closed combustion system that is used on a great many modern gas-fired hearths and heaters has made traditional chimneys redundant. Closed combustion systems draw in the air that is required for the combustion through a combined inlet/outlet duct. This means that it is simple to install the flue through a wall in many cases.
The new DRU PowerVent® system has increased the options for the placement of a gas-fired hearth. This system makes it possible for you to span horizontal gaps up to 20 metres, make a great many bends and even remove the flue gasses through the crawl space or a lower storey. Moreover, the diameter of the duct is significantly smaller than the existing ducts, and this makes it even easier to conceal, giving you the option to place a gas-fired hearth almost anywhere! For more information on this system, refer to this page ………(RON LINK!!)