We report the detection of CO ($J$=3$\to$2) line emission from all three multiple images (A,B and C) of the intrinsically faint ($\simeq$ 0.8 mJy) submillimeter-selected galaxy SMM J16359+6612. The brightest source of the submm continuum emission (B) also corresponds to the brightest CO emission, which is centered at $z$=2.5168, consistent with the pre-existing redshift derived from \Ha. The observed CO flux in the A, B and C images is 1.2, 3.5 and 1.6 Jy \kms respectively, with a linewidth of $500\pm 100$ \kms. After correcting for the lensing amplification, the CO flux corresponds to a molecular gas mass of $\sim 2\times 10 ^{10} h_{71}^{-2}$ \Msun, while the extent of the CO emission indicates that the dynamical mass of the system $\sim9\times10^{10}$ \Msun. Two velocity components are seen in the CO spectra; these could arise from either a rotating compact ring or disk of gas, or merging substructure. The star formation rate in this galaxy was previously derived to be $\sim$100--500 \Msun \yr. If all the CO emission arises from the inner few kpc of the galaxy and the galactic CO-to-H$_2$ conversion factor holds, then the gas consumption timescale is a relatively short 40 Myr, and so the submm emission from SMM J16359+6612 may be produced by a powerful, but short-lived circumnuclear starburst event in an otherwise normal and representative high-redshift galaxy.