We have demonstrated experimentally a Diode-Pumped Alkali Laser (DPAL) with a Raman resonance induced dip in the center of the gain profile, in order to produce an anomalous dispersion, necessary for making the laser superluminal. Numerical calculations match closely with experimental results, and indicate that the laser is operating superluminally, with the group index far below unity (~0.00526) at the center of the dip. The estimated factor of enhancement in the sensitivity to cavity length perturbation is ~190, approximately equaling the inverse of the group index. This enhancement factor can be made much higher via optimal tuning of parameters. Such a laser has the potential to advance significantly the field of high-precision metrology, with applications such as vibrometry, accelerometry, and rotation sensing.