A multiple input, multiple output (MIMO) radar emits probings signals with multiple transmit antennas and records the reflections from targets with multiple receive antennas. Estimating the relative angles, delays, and Doppler shifts from the received signals allows to determine the locations and velocities of the targets. Standard approaches to MIMO radar based on digital matched filtering or compressed sensing only resolve the angle-delay-Doppler triplets on a $(1/(N_T N_R), 1/B,1/T)$ grid, where $N_T$ and $N_R$ are the number of transmit and receive antennas, $B$ is the bandwidth of the probing signals, and $T$ is the length of the time interval over which the reflections are observed. In this work, we show that the \emph{continuous} angle-delay-Doppler triplets and the corresponding attenuation factors can be recovered perfectly by solving a convex optimization problem. This result holds provided that the angle-delay-Doppler triplets are separated either by $10/(N_T N_R-1)$ in angle, $10.01/B$ in delay, or $10.01/T$ in Doppler direction. Furthermore, this result is optimal (up to log factors) in the number of angle-delay-Doppler triplets that can be recovered.