We propose new nonlinear optical techniques as probes of the chirality of surfaces and thin films. The techniques are based on surface second-harmonic generation using focused laser beams. To avoid coupling to the possible anisotropy of the sample, which can also lead to chiral signals and is therefore a problem of traditional second-harmonic probes of surface chirality, the optical beams are applied at normal incidence and possess azimuthal symmetry about the direction of propagation. The handedness is obtained by using incident beams that are circularly polarized or appropriate superpositions of radially and azimuthally polarized higher-order modes. We model numerically four cases of different sample symmetries and demonstrate that the techniques are sensitive only to the chirality and not to the anisotropy. The techniques are therefore absolute probes of surface chirality and are naturally applicable to the microscopy of chiral properties of thin films.