We study extremal black hole solutions of D = 5 Gauss-Bonnet gravity coupled to a system of gauge and scalar fields. As in Einstein gravity, we find that the values of the scalar fields on the horizon must extremize a certain effective potential that depends on the black hole charges. If the matrix of second derivatives of the effective potential at this extremum has positive eigenvalues, we give evidence, based on a near horizon perturbative expansion, that the attractor mechanism continues to hold in this general class of theories. We numerically construct solutions to a particular simple single scalar field model that display the attractor mechanism over a wide range of asymptotic values for the scalar field. We also numerically construct non-extremal solutions and show that the attractor mechanism fails to hold away from extremality.