It's always hard to hear that a co-worker is talking badly about you behind your back.
Approach the person when he or she is alone. Farley suggests opening with: "There's something I need to discuss with you. Is there a time we can speak privately? It's of some importance."
When you sit down to talk, don't start a battle. Instead, say: "Some things have been getting back to me. I can imagine they aren't true, but perhaps there is some element that is true. Rather than stew about it, I wanted to come to you directly. I've been hearing you say (XYZ)."
If the gossip is related to a personal issue that you told the co-worker, explain that you told him or her in confidence. If the gossip is mean and untrue, approach the situation by saying, "Did I do something to upset you? If you have any issues with me I'd appreciate if you'd come to me first, in the future."
If the issue persists after your discussion, talk to your manager or someone from human resources.