We report the trapping of neutral atoms in a permanent magnet trap. Approximately 1×10˄8 ground-state lithium atoms have been confined in a nonzero magnetic-field minimum produced by six permanent magnets in an Ioffe configuration. These atoms have a kinetic temperature of 1.1 mK and a peak density of approximately 3×10˄9 cm˄−3. The trapped-atom lifetime is 240 s, limited by collisions with background gas. This trap provides an environment in which quantum-statistical effects, atomic collisions, and other ultralow-temperature phenomena can be studied.