We have demonstrated a laser in which the frequency shift due to small cavity fluctuations is far less than what would be expected from a conventional laser. The factor of sensitivity suppression is inferred to be equal to the effective group index experienced by the laser, implying that this laser is subluminal. We have observed a suppression factor as high as 663. Such a laser is highly self-stabilized compared to a conventional laser, and is expected to have a far smaller Schawlow-Townes linewidth. As a result, this laser may have potentially significant applications in the fields of high-precision optical metrology and passive frequency stabilization.