We present the first detection of a large quantity of molecular gas in the extended tail of an interacting galaxy. Using the NRAO 12 m telescope, we have detected CO (1–0) at five locations in the eastern tail of the peculiar starburst galaxy NGC 2782. The CO velocities and narrow (FWHM ~ 50 km s^-1) line widths in these positions agree with those seen in H I, which confirms that the molecular gas is indeed associated with the tail rather than the main disk. As noted previously, the gas in this tail has an apparent "counterrotation" compared to gas in the core of the galaxy, probably because the tails do not lie in the same plane as the disk. Assuming the standard Galactic conversion N/I_CO factor, these observations indicate a total molecular gas mass of 6 × 10⁸ M in this tail. This may be an underestimate of the total H₂ mass if the gas is metal poor. This molecular gas mass, and the implied H₂/H I mass ratio of 0.6, are higher than that found in many dwarf irregular galaxies. Comparison with an available Hα map of this galaxy, however, shows that the rate of star formation in this feature is extremely low relative to the available molecular gas, compared to L_Hα/M values for both spiral and irregular galaxies. Thus, the timescale for depletion of the gas in this feature is very long.