We had always intended to expose the surface-area info in Chimera, but once it became clear that we were going to replace MSMS with our own library (due to reliability issues) we decided to wait for the new library before doing that work.  Unfortunately the new library has been a long time in coming and is still not ready.

What you can do right now is use the Measure Volume and Area tool to get the area of an entire surface.  If you need per-atom/residue values, then you can use Area/Volume from Web (which uses the NIH StrucTools server) to get per-atom values assigned as attributes to atoms.  To get per-residue sums, you would use the sum() function of the Attribute Calculator tool to compute those and to save them (or the atom attibutes) to a file.  Part II of the Attributes tutorial (http://www.cgl.ucsf.edu/chimera/docs/UsersGuide/tutorials/attributes.html#part2) covers using the Area/Volume from Web and Attribute Calculator tools, though it use them to compute a convexity attribute rather than the residue area.

--Eric