Schwinger-Dyson equations have been used to investigate the dynamical
breaking of chiral symmetry in quantum R-2-gravity on the hat backgrou
nd. The dynamical mass generation has been shown to exist in both 2-D
and 4-D cases. This phenomenon has been noted to take place in a diffe
rent gauge in spite of the gauge dependence of the qualitative values
caused by using the ladder approximation. The numerical analysis of th
e model phase structure has been done in details.