Probably not, unless they have a static IP address. Most ISPs and even cable companies assign dynamic IP addresses in order to conserve IPs and to prevent users from hosting web sites and file servers.
If they should have a static IP, or you are contacting them when you know the IP address you have is current, there are programs, like netmeeting (I think) and some IP telephony packages that let you type in an IP address to make a "call", but the other person would already have to have the software for this to work.
If you're just wanting to trace their location, you can try a WHOIS lookup, which will give you a general idea of where the server they're using is located, or a TRACERT that shows the internet hops from your PC to that IP address.
I'm sure there are other utilites that do similar things, but the bottom line is, if you want to chat with that person, they'd have to have the same software you were using in order to connect.