Measurements of the periods of pulsars, and of their rate of change with time, are essential in understanding pulsar evolution. For binary pulsars, such as PSR1620-26 in the core of the globular cluster M4, orbital parameters can also be derived from timing measurements. Here we report the results of timing observations of PSR1620 -26, including a first determination of its period derivative P = 3.2+/-0.4x 10-19ss-1 and its orbital eccentricity e = 0.025316 +/-0.000003. The age of this millisecond pulsar is less than 2.2 × 108 years. The relatively high eccentricity is probably a result of gravitational encounters with other stars in the cluster during this time.