We present Chandra X-ray Observatory imaging observations of the young Galactic supernova remnant G11.2-0.3. The image shows that the previously known young 65-ms X-ray pulsar is at position (J2000) RA 18h 11m 29.22s, DEC -19o 25 27.6, with 1 sigma error radius 0.6. This is within 8 of the geometric center of the shell. This provides strong confirming evidence that the system is younger, by a factor of ~12, than the characteristic age of the pulsar. The age discrepancy suggests that pulsar characteristic ages can be poor age estimators for young pulsars. Assuming conventional spin down with constant magnetic field and braking index, the most likely explanation for the age discrepancy in G11.2-0.3 is that the pulsar was born with a spin period of ~62 ms. The Chandra image also reveals, for the first time, the morphology of the pulsar wind nebula. The elongated hard-X-ray structure can be interpreted as either a jet or a Crab-like torus seen edge on. This adds to the growing list of highly aspherical pulsar wind nebulae and argues that such structures are common around young pulsars.