We report the results of simultaneous observations of the Vela pulsar in X-rays and radio from the RXTE satellite and the Mount Pleasant Radio Observatory in Tasmania. We sought correlations between Vela's X-ray emission and radio arrival times on a pulse-by-pulse basis. At a confidence level of 99.8% we have found significantly higher flux density in Vela's main X-ray peak during radio pulses that arrived early. This excess flux shifts to the "trough" following the second X-ray peak during radio pulses that arrive later. Our results suggest that the mechanism producing the radio pulses is intimately connected to the mechanism producing X-rays. Current models using resonant absorption of radio emission in the outer magnetosphere as a cause of the X-ray emission are explored as a possible explanation for the correlation.