The quark structure of the f2(1270) meson has, for many years, been assumed to be a pure quark-antiquark (qq⁻) resonance with quantum numbers JPC = 2++. Recently, it was proposed that the f2(1270) is a molecular state made from the attractive interaction of two mesons. Such a state would be expected to decay strongly to final states with charged pions due to the dominant decay → π+π-, whereas decay to two neutral pions would likely be suppressed. Here, we measure for the first time the reaction p -\u3e π0π0p, using the CEBAF Large Acceptance Spectrometer detector at Jefferson Lab for incident beam energies between 3.6 and 5.4 GeV. Differential cross sections, dσ/dt, for f2(1270) photoproduction are extracted with good precision due to low backgrounds and are compared to theoretical calculations