Ultrathin (sub-monolayer to 12 monolayers) AlN nanosheets are grown epitaxially by plasma assisted molecular beam epitaxy on Ag(111) single crystals. Electron diffraction and scanning tunneling microscopy provide evidence that AlN on Ag adopts a graphite-like hexagonal structure with a larger lattice constant compared to bulk-like wurtzite AlN. This claim is further supported by ultraviolet photoelectron spectroscopy indicating a reduced energy bandgap as expected for hexagonal AlN.