  We have frequency stabilized a Coherent CR699-21 dye laser to a transient
spectral hole on the 606 nm transition in Pr^{+3}:Y_2SiO_5. A frequency
stability of 1 kHz has been obtained on the 10 microsecond timescale together
with a long-term frequency drift below 1 kHz/s. RF magnetic fields are used to
repopulate the hyperfine levels allowing us to control the dynamics of the
spectral hole. A detailed theory of the atomic response to laser frequency
errors has been developed which allows us to design and optimize the laser
stabilization feedback loop, and specifically we give a stability criterion
that must be fulfilled in order to obtain very low drift rates. The laser
stability is sufficient for performing quantum gate experiments in
Pr^{+3}:Y_2SiO_5.
