  Deep inelastic electron-photon scattering is studied using e+e- data
collected by the OPAL detector at centre-of-mass energies sqrt{s_ee} ~ M_{Z^0}.
The photon structure function F_2^gamma(x,Q^2) is explored in a Q^2 range of
1.1 to 6.6 GeV/c^2 at lower x values than ever before. To probe this kinematic
region events are selected with a beam electron scattered into one of the OPAL
luminosity calorimeters at scattering angles between 27 and 55 mrad. A
measurement is presented of the photon structure function F_2^gamma(x,Q^2) at
<Q^2> = 1.86 GeV^2 and 3.76 GeV^2 in five logarithmic x bins from 0.0025 to
0.2.
