The gapless edge states have been found in a 2D molecular system built with light atoms: C,O,H. This prediction is done on the basis of combined density functional theory (DFT) and tight-binding calculations. The system does not exhibit any effect of the spin-orbit coupling (SOC), neither intrinsic nor Rashba type. The band structure and the edge states are tuned with a strength of the p-stacking and O...H interactions. The elementary cell of this noncovalent structure, does not have the 3D inversion or rotational symmetry. Instead, the system transforms via a superposition of two reflections: with respect to the xz and xy mirror planes, both containing the non-periodic direction. This superposition is equivalent to the inversion in the 2D subspace, in which the system is periodic. The energy gap obtained with the DFT method is 0.11 eV, and largely opens (above 1 eV) with the GW and hybrid-DFT approaches. The bands inversion is partial, i.e. the Bloch states are mixed, with the "swapping" and "non-swapping" atomic contributions.