Thin films of pure metals and alloys can adopt phases that differ from those of the corresponding bulk alloy phase diagram. In the bulk, PdzCu1-z adopts a B2 phase (CsCl structure) for 0.35 < z < 0.55, in spite of the fact that pure Pd and Cu both have face centered cubic (FCC) bulk crystal structures. Herein, we demonstrate that this transition to the B2 phase is suppressed in thin film PdzCu1-z alloys with thickness < 6 nm. Spatially resolved X-ray photoemission spectroscopy was used to map the Cu 2p(3/2) core level shifts (CLS, Delta ECLSCu(z)) across a PdzCu1-z composition spread alloy film (CSAF) as a function of both composition and film thickness. In the FCC phase, the Cu 2p(3/2) binding energy decreases monotonically across the range z = 0 -> 1. At T < 873 K, there is an additional discontinuous CLS over the composition range of the B2 phase, 0.35 < z < 0.55. Thus, the Cu 2p(3/2) CLS can be used to distinguish between the B2 and FCC phases. After annealing the PdzCu1-z CSAF to 700 K, the bulk B2 phase was observed at film thicknesses > 6 nm. However, at film thicknesses in the range 4-6 nm, only the FCC phase was observed. Stabilization of the FCC phase for films that are < 6 nm thick may be due, in part, to surface energy effects.