A search for the Theta+ in the reaction gammad --> pK-K+n was completed using the CLAS detector at Jefferson Lab. A study of the same reaction, published earlier, reported the observation of a narrow Theta+ resonance. The present experiment, with more than 30 times the integrated luminosity of our earlier measurement, does not show any evidence for a narrow pentaquark resonance. The angle-integrated upper limit on Theta+ production in the mass range of 1.52-1.56 GeV/c2 for the gammad --> pK-Theta+ reaction is 0.3 nb (95% C.L.). This upper limit depends on assumptions made for the mass and angular distribution of Theta+ production. Using Lambda(1520) production as an empirical measure of rescattering in the deuteron, the cross section upper limit for the elementary gamman --> K-Theta+ reaction is estimated to be a factor of 10 higher, i.e., approximately 3 nb (95% C.L.).