We report the discovery of LSR 0602+3910, an L dwarf of class L1. The object was initially identified by Lépine et al. as a new high proper motion star lying close to the Galactic plane. Its Two Micron All Sky Survey value of J-Ks = 1.43 is consistent with an L dwarf, which we now confirm spectroscopically. In addition, we see a signature of Li I absorption, making LSR 0602+3910 a brown dwarf, one of the brightest known (Ks = 10.86). Among L dwarfs, it is second in brightness to the combined light of 2MASS 0746+20, a close binary system. We see no indication that LSR 0602+3910 is a binary, although high-resolution imaging will be required to confirm this. Spectroscopic and photometric distance estimates agree very well, placing LSR 0602+3910 at d = 10.6 ± 0.8 pc. LSR 0602+3910 was most likely missed in previous searches because of its proximity to the plane, the region that most searches avoided. We estimate that some 40% of bright L dwarfs are missed because of this selection effect.