  The half-life of \tsups{37}K has been measured to be
$1.23651(94)~\mathrm{s}$, a value nearly an order of magnitude more precise
than the best previously reported. The $\beta^+$ decay of \tsups{37}K occurs
mainly via a superallowed branch to the ground-state of its $T=1/2$ mirror,
\tsups{37}Ar. This transition has been used recently, together with similar
transitions from four other nuclei, as an alternative test of CVC and method
for determining $V_{ud}$, but the precision of its $ft$ value was limited by
the relatively large half-life uncertainty. Our result corrects that situation.
Another motivation for improving the $ft$ value was to determine the
standard-model prediction for the $\beta$-decay correlation parameters, which
will be compared to those currently being measured by the \trinat{}
collaboration at \triumf. The new $ft$ value, $4605(8)~\mathrm{s}$, is now
limited in precision by the $97.99(14)\%$ ground-state branching ratio.
