A hybrid disklike/rodlike molecule comprising central triphenylene core symmetrically substituted with six azobenzene moieties (C-12) has been adsorbed at the 1,2,4-trichlorobenzene/Au(111) interface, revealing the potential of azobenzene moieties for the control of two-dimensional (2D) chiral networks. The C-12, which due to its complex molecular structure possesses a relatively large number of degrees of freedom, surprisingly forms monolayers of only one kind of structure, namely a hexagonal network of large period, 3.5 nm. By combining scanning tunneling microscopy (STM) and DFT calculations, we evidence that this specific 2D-ordering is due to cooperative weak hydrogen bonds between neighboring azobenzenes and azobenzene-Au(111) interactions. The crystallographic network is hexagonal, but azobenzene-azobenzene pairing, associated with hydrogen bonding renders the network chiral with a chirality spanning all ranges, from the molecular C-12 configuration, to the configuration of the azobenzene dimers, the rosettelike azobenzene network and the C-12 network orientation on Au(111) rotated by ±8° from the main crystallographic direction Au<110>, depending on the handedness of the molecular network. This chiral 2D system thus paves the way for the formation of macroscopic 2D molecular crystals of unique handedness, if additional enantiomeric chiral dopants can be used.