David had good suggestions, but if you just want the center with equal weights for each atom then you can use Chimera's 'cofr' command to get that if you're careful.  For instance:

cofr :10.a & aromatic ring

will report the center of the aromatic ring in residue 10 of chain A to the status line and to the Reply Log.  However, it reports it in lab coordinates, not model coordinates, so you have to be careful not to move your model after opening it -- so that the model and lab coordinates are the same.  If you do move it, you should be able to use the "reset" command to get the coordinate systems back in sync.  This presumes that you don't have other models open.

--Eric