  A key limiting factor of present day state-of-the-art laser frequency
stabilization using Fabry-P\'erot cavities are length changes due to
thermo-mechanical noise, originating from, for example, Brownian motion. We
present a laser-frequency stabilization concept using an optical cavity with a
strong slow-light effect to reduce the impact of cavity length changes on the
frequency stability. The resulting noise-reduction factor is proportional to
the ratio between the light phase and group velocities in the highly dispersive
cavity spacer. We experimentally demonstrate a proof-of-principle
implementation of this laser-frequency stabilization technique using a
rare-earth doped crystalline cavity spacer in conjunction with semi-permanent
spectral tailoring to achieve precise control of the dispersive properties of
the cavity. A reduction in frequency sensitivity of four orders of magnitude
was achieved compared to the same setup in the absence of the slow-light
effect.
