Using archival X-ray observations and a log-normal population model, we estimate constraints on the intrinsic scatter in halo mass at fixed optical richness for a galaxy cluster sample identified in Dark Energy Survey Year-One (DES-Y1) data with the redMaPPer algorithm. We examine the scaling behavior of X-ray temperatures, $T_X$, with optical richness, $lambda_{RM}$, for clusters in the redshift range $0.2<z<0.7$. X-ray temperatures are obtained from Chandra and XMM observations for 58 and 110 redMaPPer systems, respectively. Despite non-uniform sky coverage, the $T_X$ measurements are $> 50%$ complete for clusters with $lambda_{RM} > 130$. Regression analysis on the two samples produces consistent posterior scaling parameters, from which we derive a combined constraint on the residual scatter, $sigma_{ln Tx | lambda} = 0.275 pm 0.019$. Joined with constraints for $T_X$ scaling with halo mass from the Weighing the Giants program and richness--temperature covariance estimates from the LoCuSS sample, we derive the richness-conditioned scatter in mass, $sigma_{ln M | lambda} = 0.30 pm 0.04, _{({rm stat})} pm 0.09, _{({rm sys})}$, at an optical richness of approximately 70. Uncertainties in external parameters, particularly the slope and variance of the $T_X$--mass relation and the covariance of $T_X$ and $lambda_{RM}$ at fixed mass, dominate the systematic error. The $95%$ confidence region from joint sample analysis is relatively broad, $sigma_{ln M | lambda} in [0.14, , 0.55]$, or a factor ten in variance.
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