Ablative Rayleigh-Taylor instability growth was investigated to elucidate the fundamental physics of thermal conduction suppression in a magnetic field. Experiments found that unstable modulation growth is faster in an external magnetic field. This result was reproduced by a magnetohydrodynamic simulation based on a Braginskii model of electron thermal transport. An external magnetic field reduces the electron thermal conduction across the magnetic field lines because the Larmor radius of the thermal electrons in the field is much shorter than the temperature scale length. Thermal conduction suppression leads to spatially nonuniform pressure and reduced thermal ablative stabilization, which in turn increases the growth of ablative Rayleigh-Taylor instability.