  The first measurement of diffractive scattering of quasi-real photons with
large momentum transfer gamma p -> gamma Y, where Y is the proton dissociative
system, is made using the H1 detector at HERA. The measurement is performed for
initial photon virtualities Q^2 < 0.01 GeV^2. Cross sections are measured as a
function of W, the incident photon-proton entre of mass energy, and t, the
square of the four-momentum transferred at the proton vertex, in the range 175
< W < 247 GeV and 4<|t|<36 GeV^2. The W dependence is well described by a model
based on perturbative QCD using a leading logarithmic approximation of the BFKL
evolution. The measured |t| dependence is harder than that predicted by the
model and those observed in exclusive vector meson production.
