ASK HN: I'm being accused of trademark infringement. What should I do?

I recently bought a premium domain name to launch a new market place for food lovers to discover new food & beverages products. I bought it from a domain squatter for a little over a couple of grand and thought I got a pretty good deal on it. It turns out the domain name contains a word that a major fast food company has a trademark on and they are demanding I close the the website because they feel it interferes with their trademark and confuses their customers. They are also demanding that I transfer the domain name to them or they will take legal action.

First of all, the original owner registered the domain in 2002, way before they registered their trademark in 2006. It was then transfered to me early this year. Who has the rights to the domain?

Also, I do not have the power to go up against a big company so what do you think I should do?