We report a sensitive search for redshifted CO J = 3-2 emission from the weak radio galaxy 53W002 at z = 2.394. Maps at resolutions of 3'' and 235 km s-1 show a significant emission peak within 0farcs5 of the optical and radio continuum peaks. The measured narrowband flux is approximately 10 times the extrapolated centimeter-wavelength nonthermal radio continuum expected at 101.9 GHz and exhibits a spectral profile implying a 540 km s-1 width (FWHM) at a systemic redshift z = 2.394 ± 0.001 for CO (3-2). This emission has a total integrated flux of 1.51 ± 0.2 Jy km s-1, approximately 4 times weaker than that previously seen in the lensed systems FSC 10214+4724 and the Cloverleaf QSO. For a Galactic CO-to-H2 conversion ratio, the implied molecular gas mass is 7.4 × 1010 Msun (H0 = 75 km s-1 Mpc-1 and q0 = 0.5). The CO emission is elongated at P.A. = 120° with a deconvolved major-axis radius of 15 kpc (2farcs8). This extension is along a similar direction to that seen in the centimeter-wave radio continuum and in the optical, but approximately 3 times larger. A velocity gradient is seen along the major axis, and if this structure is a (forming) disk, the implied dynamical mass is (9-22) × 1010 Msun at r ≤ 15 kpc, assuming inclination i = 0° (edge-on). The magnitude of these masses and the similarity of the high gas-mass fraction are consistent with the host galaxy of 53W002 being a young galactic system but the metallicity (probably ≥0.1 Zsun in order to produce the CO lines) implies significant heavy-element production prior to z = 2.4. This constitutes the first high redshift molecular gas detected in emission where there is probably no gravitational magnification.