Representing unresolved moist convection in coarse-scale climate models remains one of the main bottlenecks of current climate simulations. Many of the biases present with parameterized convection are strongly reduced when convection is explicitly resolved (i.e., in cloud resolving models at high spatial resolution approximately a kilometer or so). We here present a novel approach to convective parameterization based on machine learning, using an aquaplanet with prescribed sea surface temperatures as a proof of concept. A deep neural network is trained with a superparameterized version of a climate model in which convection is resolved by thousands of embedded 2-D cloud resolving models. The machine learning representation of convection, which we call the Cloud Brain (CBRAIN), can skillfully predict many of the convective heating, moistening, and radiative features of superparameterization that are most important to climate simulation, although an unintended side effect is to reduce some of the superparameterization's inherent variance. Since as few as three months' high-frequency global training data prove sufficient to provide this skill, the approach presented here opens up a new possibility for a future class of convection parameterizations in climate models that are built "top-down," that is, by learning salient features of convection from unusually explicit simulations.