  We present and publicly release (https://www.gclasshst.com) the first
spatially resolved H$\alpha$ maps of star-forming cluster galaxies at $z\sim1$,
made possible with the Wide Field Camera 3 (WFC3) G141 grism on the Hubble
Space Telescope (HST). Using a similar but updated method to 3D-HST in the
field environment, we stack the H$\alpha$ maps in bins of stellar mass, measure
the half-light radius of the H$\alpha$ distribution and compare it to the
stellar continuum. The ratio of the H$\alpha$ to stellar continuum half-light
radius, $R[\mathrm{H}\alpha/\mathrm{C}]=\frac{R_{\mathrm{eff,
H}\alpha}}{R_{\mathrm{eff, Cont}}}$, is smaller in the clusters by $(6\pm9)\%$,
but statistically consistent within $1\sigma$ uncertainties. A negligible
difference in $R[\mathrm{H}\alpha/\mathrm{C}]$ with environment is surprising,
given the higher quenched fractions in the clusters relative to the field. We
postulate that the combination of high quenched fractions and no change in
$R[\mathrm{H}\alpha/\mathrm{C}]$ with environment can be reconciled if
environmental quenching proceeds rapidly. We investigate this hypothesis by
performing similar analysis on the spectroscopically-confirmed recently
quenched cluster galaxies. 87% have H$\alpha$ detections, with star formation
rates $8\pm1$ times lower than star-forming cluster galaxies of similar stellar
mass. Importantly, these galaxies have a $R[\mathrm{H}\alpha/\mathrm{C}]$ that
is $(81\pm8)\%$ smaller than coeval star-forming field galaxies at fixed
stellar mass. This suggests the environmental quenching process occurred
outside-in. We conclude that disk truncation due to ram-pressure stripping is
occurring in cluster galaxies at $z\sim1$, but more rapidly and/or efficiently
than in $z\lesssim0.5$ clusters, such that the effects on
$R[\mathrm{H}\alpha/\mathrm{C}]$ become observable just after the cluster
galaxy has recently quenched.
