High-order harmonic generation by a bicircular field, which consists of two coplanar counterrotating circularly polarized fields of frequency rω and sω (r and s are integers), is investigated for a polyatomic molecule. This field possesses dynamical symmetry, which can be adapted to the symmetry of the molecular Hamiltonian and used to investigate the molecular symmetry. For polyatomic molecules having the Cr+s symmetry only the harmonics n = q(r+s)±r, q = 1, 2, . . ., are emitted having the ellipticity εn = ±1. We illustrate this using the example of the planar molecules BH3 and BF3, which obey the C3 symmetry. We show that for the BF3 molecule, similarly to atoms with a p ground state, there is a strong asymmetry in the emission of high harmonics with opposite helicities. This asymmetry depends on the molecular orientation.