We have extensively searched for periodic signals in the area of the soft gamma-ray repeater SGR 1900+14, at 430 and 1410 MHz with the Arecibo telescope. Our observations did not reveal the 5.16-s periodicity reported for the magnetar down to a 430-MHz flux density limit of 150 μJy. During the search we discovered a 226-ms radio pulsar, PSR J1907+0918. The period derivative implies the characteristic age for this pulsar is only 38 kyr. Independent evidence in support of this apparent youth are the unusually high degree of circular polarization and its relatively flat radio spectrum. The close proximity of PSR J1907+0918 to SGR 1900+14 suggests that they may have evolved from a massive binary system. Regardless of this possibility, it is presently not clear to us that SGR 1900+14 is associated with the supernova remnant G42.8+0.6.