Where are you finding the MAC address? Your DHCP server or the switch?
1.) Are your switches manageable? If so get a console session session and look up the offensive MAC address. It will be assigned to a port. On a Cisco device the command is sho mac. On switches with http interfaces you find the menu option for port addresses. If the port that the MAC address appears on is also the port that is cross connected to another switch, move on to the next switch and repeat the process. Identifying the port will lead you directly to the machine. Depending on the switches that you use you can also deny access to that MAC address and pretty soon you would assume someone will start complaining about their access. (Or block the ip addresses at your router/firewall and wait for the complaint.)
2.) If you have a RAS or some kine of dial in server it is very possible that that server is obtaining multiple addresses in proxy for the dial in clients and you have no problem.
3.) Another giveaway as to the identity would be to check the ARP table on your router. See if the MAC address appears with any other IP addresses outside of what your DHCP range is. If it is a dialup/RAS server, I would imagine that the device also has a static IP address which chould be identified in the ARP table. (That assumes that the server is in the routers ARP cache.)
4.) And a last idea, I don't know if it is possible with DHCP, but can you reserve an invalid IP address for that MAC address and then sit back and wait for the user to compalin?