The evolution leading to the formation of a neutron star in the very young Westerlund 1 star cluster is investigated. The turnoff mass has been estimated to be ~35 M, indicating a cluster age ~3-5 Myr. The brightest X-ray source in the cluster, CXO J164710.2–455216, is a slowly spinning (10 s) single neutron star and potentially a magnetar. Since this source was argued to be a member of the cluster, the neutron star progenitor must have been very massive (M_ZAMS 40 M), as noted by Muno et al. Since such massive stars are generally believed to form black holes (rather than neutron stars), the existence of this object poses a challenge for understanding massive star evolution. We point out that, while single-star progenitors below M_ZAMS 20 M form neutron stars, binary evolution completely changes the progenitor mass range. In particular, we demonstrate that mass loss in Roche lobe overflow enables stars as massive as 50-80 M, under favorable conditions, to form neutron stars. If the very high observed binary fraction of massive stars in Westerlund 1 (70%) is considered, it is natural that CXO J164710.2–455216 was formed in a binary which was disrupted in a supernova explosion, such that it is now found as a single neutron star. Hence, the existence of a neutron star in a given stellar population does not necessarily place stringent constraints on progenitor mass when binary interactions are considered. It is concluded that the existence of a neutron star in the Westerlund 1 cluster is fully consistent with the generally accepted framework of stellar evolution.