  We have carried out VLA imaging and a Fermi timing analysis of the 115 ms
gamma-ray and radio pulsar PSR J0002+6216. We found that the pulsar lies at the
apex of a narrowly collimated cometary-like 7 arcmin tail of non-thermal radio
emission which we identify as a bow-shock pulsar wind nebula. The tail of the
nebula points back toward the geometric center of the supernova remnant CTB 1
(G116.9+0.2) 28 arcmin away, at a position angle $\theta_\mu=113^\circ$. We
measure a proper motion with 2.9$\sigma$ significance from a Fermi timing
analysis giving $\mu$=115$\pm$33 mas yr$^{-1}$ and
$\theta_\mu=121^\circ\pm{13}^\circ$, corresponding to a large transverse pulsar
velocity of 1100 km s$^{-1}$ at a distance of 2 kpc. This proper motion is of
the right magnitude and direction to support the claim that PSR J0002+6216 was
born from the same supernova that produced CTB 1. We explore the implications
for pulsar birth periods, asymmetric supernova explosions, and mechanisms for
pulsar natal kick velocities.
