The exclusive reaction γp→K̄0K+n was studied in the photon energy range between 1.6 and 3.8 GeV searching for evidence of the exotic baryon Θ+(1540)→nK+. The decay to nK+ requires the assignment of strangeness S=+1 to any observed resonance. Data were collected with the CLAS detector at the Thomas Jefferson National Accelerator Facility corresponding to an integrated luminosity of 70pb-1. No evidence for the Θ+ pentaquark was found. Upper limits were set on the production cross section as function of center-of-mass angle and nK+ mass. The 95% C.L. upper limit on the total cross section for a narrow resonance at 1540 MeV was found to be 0.8 nb.