  We report the laser cooling of a single $^{40}\text{Ca}^+$ ion in a Penning
trap to the motional ground state in one dimension. Cooling is performed in the
strong binding limit on the 729-nm electric quadrupole $S_{1/2}\leftrightarrow
D_{5/2}$ transition, broadened by a quench laser coupling the $D_{5/2}$ and
$P_{3/2}$ levels. We find the final ground state occupation to be $98\pm1\%$.
We measure the heating rate of the trap to be very low with
$\dot{\bar{n}}\approx 0.3\pm0.2\textrm{s}^{-1}$ for trap frequencies from
$150-400\textrm{kHz}$, consistent with the large ion-electrode distance.
