The local (R < 3 kpc) rate of core collapse supernovae during the last millennium appears to be significantly higher than that derived from the bright end of luminosity function of Scalo (1986), and the assumption that all stars with main-sequence masses greater than 8 script M sign⊙ (or 5 script M sign⊙) become supernovae. This dilemma might be resolved by assuming that either (1) the lower limit to the main-sequence masses of supernova precursors is lower than previously estimated, (2) the bright end of the stellar luminosity function near the Sun is a few times more populous than previously believed, (3) the distances of some nearby supernovae have been underestimated, or (4) mass transfer in close binaries adds significantly to the pool of objects with masses large enough to explode as core-collapse supernovae. Possibly all four of these factors conspire to increase the predicted rate of 0.3 (or 0.7) core-collapse supernovae per millennium within 3 kpc to a value that is closer to the observed rate of three to four such objects during the last 1000 years. A relatively high supernova rate in the solar neighborhood might, if real, be interpreted in two ways. Either the global Galactic supernova rate is higher than previously believed, or the local density of massive young stars is higher than its average value on the solar circle.