We report on observations of the sixth accretion-powered millisecond pulsar, IGR J00291ϩ5934, with the Rossi X-Ray Timing Explorer. The source is a faint recurrent X-ray transient initially identified by the International Gamma-Ray Astrophysics Laboratory. The 599 Hz (1.67 ms) pulsation had a fractional rms amplitude of 8% in the 2-20 keV range, and its shape was approximately sinusoidal. The pulses show an energy-dependent phase delay, with the 6-9 keV pulses arriving up to 85 ms earlier than those at lower energies. No X-ray bursts, dips, or eclipses were detected. The neutron star is in a circular 2.46 hr orbit with a very low-mass donor, most likely a brown dwarf. The binary parameters of the system are similar to those of the first known accreting millisecond pulsar, SAX J1808.4Ϫ3658. Assuming that the mass transfer is driven by gravitational radiation and that the 2004 outburst fluence is typical, the 3 yr recurrence time implies a distance of at least 4 kpc.