We examine here a novel yet simple technique for monitoring changes in global mean sea level over periods of weeks to years with an accuracy of a few centimeters using altimeter data from a well-tracked satellite. The technique is based on the following argument. A satellite's orbit period and hence, the mean semimajor axis of the orbit, are accurately determined by tracking systems located on the earth's surface. With laser or radiometric tracking systems, the mean semimajor axis can be determined with an accuracy of better than a centimeter. If the satellite carries an accurate altimeter, the difference between the mean semimajor axis and the global mean height measured by altimeter is mean sea level. Any temporal change in the measurement of sea level must be due to drift in the altimeter or to change in the volume of the sea. To demonstrate the application of this technique, the fully corrected altimeter measurements of sea level obtained by Seasat during a 24-day period when the satellite was in an exactly repeating orbit were separated into eight 3-day segments and averaged over each of these periods. The calculated mean sea level relative to the Goddard Earth Model--10B geoid varied over a range of ¿7 cm during these eight periods. The variation is due primarily to errors in the vetical component of the satellite's ephemeris, which had a standard deviation of approximately 1.3 m. The results have important consequences. The proposed Topex/Poseidon altimetric satellite mission should have an ephemeris error of around 10 cm, and the satellite's ground track will repeat every 10 days. Thus, we expect that data from this satellite could be used to monitor variations in mean sea level with an accuracy of 1 or 2 cm during the 3-- to 5--year duration of the mission. Errors in the observations will be due primarily to either drift in the altimeter or orbit error. If an alternate technique is available to monitor the altimeter drift, the measurements can be used to monitor mean sea level with an accuracy which may be sufficient to detect global climate change.