  We use a sample of 14 massive, dynamically relaxed galaxy clusters to
constrain the Hubble Constant, $H_0$, by combining X-ray and Sunyaev-Zel'dovich
(SZ) effect signals measured with Chandra, Planck and Bolocam. This is the
first such analysis to marginalize over an empirical, data-driven prior on the
overall accuracy of X-ray temperature measurements, while our restriction to
the most relaxed, massive clusters also minimizes astrophysical systematics.
For a cosmological-constant model with $\Omega_m = 0.3$ and $\Omega_{\Lambda} =
0.7$, we find $H_0 = 67.3^{+21.3}_{-13.3}$ km/s/Mpc, limited by the temperature
calibration uncertainty (compared to the statistically limited constraint of
$H_0 = 72.3^{+7.6}_{-7.6}$ km/s/Mpc). The intrinsic scatter in the X-ray/SZ
pressure ratio is found to be $13 \pm 4$ per cent ($10 \pm 3$ per cent when two
clusters with significant galactic dust emission are removed from the sample),
consistent with being primarily due to triaxiality and projection. We discuss
the prospects for reducing the dominant systematic limitation to this analysis,
with improved X-ray calibration and/or precise measurements of the relativistic
SZ effect providing a plausible route to per cent level constraints on $H_0$.
