We present a new Chandra observation of the galaxy cluster Abell 2146 which has revealed a complex merging system with a gas structure that is remarkably similar to the Bullet cluster (eg. Markevitch et al. 2002). The X-ray image and temperature map show a cool 2-3 keV subcluster with a ram pressure stripped tail of gas just exiting the disrupted 6-7 keV primary cluster. From the sharp jump in the temperature and density of the gas, we determine that the subcluster is preceded by a bow shock with a Mach number M=2.2+/-0.8, corresponding to a velocity v=2200^{+1000}_{-900} km/s relative to the main cluster. We estimate that the subcluster passed through the primary core only 0.1-0.3 Gyr ago. In addition, we observe a slower upstream shock propagating through the outer region of the primary cluster and calculate a Mach number M=1.7+/-0.3. Based on the measured shock Mach numbers M~2 and the strength of the upstream shock, we argue that the mass ratio between the two merging clusters is between 3 and 4 to one. By comparing the Chandra observation with an archival HST observation, we find that a group of galaxies is located in front of the X-ray subcluster core but the brightest cluster galaxy is located immediately behind the X-ray peak.