If someone falsely tells someone that a store is closing, is that slander, and can I take legal action?

I own a store in a small town. It's a service industry and people book my service in advance. A customer of mine called to tell me she heard I was going out of business. She heard it from someone in the neighborhood. It's 100% false. Completely fabricated. But if that rumor got around, I would lose a lot of potential business, and could risk my livelihood.