The parity-nonconservation (PNC) effect on the laser-induced 2 3S1-2 1S0 transition in heavy heliumlike ions is considered. A simple analytical formula for the PNC correction to the cross section is derived for the case, when the opposite-parity 21S0 and 23P0 states are almost degenerate and, therefore, the PNC effect is strongly enhanced. Numerical results are presented for heliumlike gadolinium and thorium, which seem the most promising candidates for such experiments. In both Gd and Th cases the photon energy required will be anticipated with a high-energy laser built at GSI. Alternatively, it can be gained with ultraviolet lasers utilizing relativistic Doppler tuning at FAIR facilities in Darmstadt.