High magnetic field (0.5 T to 9 T) measurements of the in-plane transport critical current density J(c) of YBa2Cu3O7 at liquid nitrogen temperature are reported as a function of the orientation of magnetic field B with respect to the a,b,plane. In contrast to earlier results at lower fields (< 3 T), the measurements reported here at high fields reveal a J(c) versus angle curve with a head-and-shoulders shape with two angular regions having distinctly different behaviour. For magnetic field oriented close to the a,b-plane, a sharp, narrow intrinsic-pinning peak in J(c) about the B perpendicular-to c-axis is observed; on either side of the peak, J(c) is still relatively high (approximately 10(4) A cm-1) and nearly independent of magnetic field magnitude and angle. However, beyond a critical angle theta(c), the J(c) versus theta dependence crosses over to a markedly different behaviour, characterized by a decrease in the sharpness of the voltage - current characteristic and a rapid decrease in J(c). The critical angle theta(c) where this change occurs is determined experimentally from the sharp break in the J(c) versus theta curve at the edge of the shoulders, defined by the angle where the minimum in d2J(c)/dtheta2 occurs. Characteristic values of theta(c) for oriented-grained YBa2Cu3O7 at 76 K are +/- 39-degrees at 5 T, +/- 24-degrees at 7 T and +/- 17-degrees at 9 T (where theta = 0 for B in the a,b-plane). To take advantage of the high, nearly field-independent J(c) on either side of the intrinsic pinning peak, magnet design will need to allow an adequate angular margin to avoid the pinning transition at theta(c).