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We report on a new Be/X-ray pulsar binary located in the Wing of the Small Magellanic Cloud (SMC). The strong pulsed X-ray source was discovered with the Chandra and XMM-Newton X-ray observatories. The X-ray pulse period of 1062 s is consistently determined from both Chandra and XMM-Newton observations, revealing one of the slowest rotating X-ray pulsars known in the SMC. The optical counterpart of the X-ray source is the emission-line star 2dFS 3831. Its B0-0.5(III)e+ spectral type is determined from VLT-FLAMES and 2dF optical spectroscopy, establishing the system as a Be/X-ray binary (Be-XRB). The hard X-ray spectrum is well fitted by a power law with additional thermal and blackbody components, the latter reminiscent of persistent Be-XRBs. This system is the first evidence of a recent supernova in the low-density surroundings of NGC602. We detect a shell nebula around 2dFS 3831 in H alpha and [OIII] images and conclude that it is most likely a supernova remnant. If it is linked to the supernova explosion that created this new X-ray pulsar, its kinematic age of (2-4) x 10(4) yr provides a constraint on the age of the pulsar.