For the eclipsing binary system CM Draconis, eclipse minimum times have been monitored with high precision between 1994 and 1999. Periodic deviations of minimum times from a linear ephemeris may indicate the presence of an orbiting third body. Individual measurements of 41 eclipse minimum times result in a standard deviation from linear ephemeris of 5.74 seconds. A power spectral analysis of the residuals reveals only one periodicity with more then 2 seconds amplitude. This feature, with a periodicity between 750 and 1050 days has an amplitude of 2.8+/-0.5 seconds, and is also present with similar phases if the power spectral analysis is performed independently for primary and secondary eclipses. It would be compatible with a circumbinary planet of 1.5 -3 Jupiter masses at an orbital distance of 1.1-1.45 AU to the binary barycenter. The assignation of a planet to the CM Dra system can however only be upheld if this periodicity can be followed in future observations for several years. For low-mass eclipsing binary stars, the method of eclipse minimum timing allows one to reach mass limits for the detection of third bodies well below that feasible by radial velocity measurements.