We report measurements of the abundance of He-3 for a sample of six Galactic planetary nebulae: IC 289, NGC 3242, NGC 6543, NGC 6720, NGC 7009, and NGC 7662. Based on observations of the 8.665 GHz hyperfine transition of He-3(+), we derive He-3/H abundances ranging from similar to-0.1 to 1.0 x 10(-3) by number. These abundances are more than an order of magnitude larger than those found in any H II region, the local interstellar medium, or the proto-solar system. If planetary nebulae are surrounded by large, low-density, ionized halos, modeling suggests that these abundances will decrease by a factor of about 2. Our source sample is highly biased in that we selected objects on the basis of several criteria that maximized the likelihood of He-3 detections. The abundances are nonetheless consistent with the idea that He-3 is produced in significant quantities by stars of 1-2 M.. We conclude that there is some stellar production of He-3.