  By extending the constant-acceleration analysis of Smith, Mao, & Paczynski to
include jerk, I show that microlens parallax measurements are subject to a
four-fold discrete degeneracy. The new degeneracy is characterized by a
projected velocity \tilde v_j =
-(3/4)\csc\beta_\ec(\cos^2\psi\sin^2\beta_\ec+\sin^2\psi)^{3/2}v_earth, where
\beta_\ec is the ecliptic latitude, \psi is the phase of the Earth's orbit
relative to opposition at the time of the event maximum, and v_earth=30 km/s is
the speed of the Earth. The degeneracy becomes important when the lens
projected velocity \tilde v is of order \tilde v_j. For events toward the Large
Magellanic Cloud, \tilde v_j\simeq (3/4)v_earth, so this degeneracy is
important primarily for lenses in the Milky Way disk. In particular, it solves
the puzzle of MACHO-LMC-5, whose microlens parallax measurement had yielded
mass and distance determinations for the lens that were inconsistent with
photometric estimates. Toward the Galactic bulge, \tilde v_j ranges from about
0.2 km/s at the solstice to about 200 km/s at the equinoxes, so the effect of
the degeneracy depends strongly on the peak time of the event. The degeneracy
applies mainly to events with Einstein timescales, t_E < yr/2pi.
