We report the discovery of a 267 ms pulsar, PSR 1853 + 01, in the supernova remnant W44 (G34.7 - 0.4). The pulsar is located south of the center of W44, well within its radio shell and at the southern edge of the X-ray emission region which fills the interior of the remnant. The period derivative P almost-equal-to 208 x 10(-15) s s-1 leads to a characteristic age of approximately 20,000 yr for the pulsar, which agrees well with the estimated age of W44 (greater-than-or-equal-to 10,000 yr). Similarly, the dispersion measure derived distance of the pulsar, approximately 3.2 kpc, is almost identical with the kinematic distance of the remnant, 3.1 kpc. As expected in the case of a young pulsar, PSR 1853 + 01 exhibits large timing activity. These data clearly indicate that the two objects are physically related and form the sixth known pulsar-supernova remnant association. We also discuss the possibility that PSR 1853 + 01 and a nearby older pulsar PSR 1854 + 00 may have a common origin in a binary system disrupted by the explosion that produced W44.