  We have made the first measurements of the virtual Compton scattering process
via the e p -> e p gamma exclusive reaction at Q**2 = 1 GeV**2 in the nucleon
resonance region. The cross section is obtained at center of mass (CM) backward
angle, theta_gamma_gamma*, in a range of total (gamma* p) CM energy W from the
proton mass up to W = 1.91 GeV. The data show resonant structures in the first
and second resonance regions, and are well reproduced at higher W by the
Bethe-Heitler+Born cross section, including t-channel pi0-exchange. At high W,
our data, together with existing real photon data, show a striking Q**2
independence. Our measurement of the ratio of H(e,e'p)gamma to H(e,e'p)pi0
cross sections is presented and compared to model predictions.
