In order to install a 3 prong receptacle you must have a ground in the box, otherwise you can install a GFCI receptacle. This will provide a 3 prong plug but still will not provide a ground.
Though before you do that you should check to make sure whether a ground exist or not. If the cable that supplies power to the receptacle box is armored cable then a ground may exist in the box. To tell you need to buy a neon bulb voltage tester or a multimeter. You measure between the hot wire and the metal box. If you get either 120 volts or a light on the tester then this indicates a ground is present in the box. Then you can install a 3 prong self grounding receptacle in place of the 2 prong. Self grounding recpetacles are sold at Home Depot and indicated on the box to be self grounding.
Your other option is to run a new circuit to the living room that has a ground and install a new receptacle.
Here's a link that'll explain all of this to you and under what conditions you can replace a 2 prong with a 3 prong.
http://www.codecheck.com/250_50_commentary.html