The emergence of two-dimensional (2D) materials launched a fascinating frontier of flatland electronics. Most crystalline atomic layer materials are based on layered van der Waals materials with weak interlayer bonding, which naturally leads to thermodynamically stable monolayers. We report the synthesis of a 2D insulator comprised of a single atomic sheet of honeycomb structure BeO (h-BeO), although its bulk counterpart has a wurtzite structure. The h-BeO is grown by molecular beam epitaxy (MBE) on Ag(111) thin films that are conveniently grown on Si(111) wafers. Using scanning tunneling microscopy and spectroscopy (STM/S), the honeycomb BeO lattice constant is determined to be 2.65 angstrom with an insulating band gap of 6 eV. Our low energy electron diffraction (LEED) measurements indicate that the h-BeO forms a continuous layer with good crystallinity at the millimeter scale. Moire pattern analysis shows the BeO honeycomb structure maintains long range phase coherence in atomic registry even across Ag steps. We find that the interaction between the h-BeO layer and the Ag(111) substrate is weak by using STS and complimentary density functional theory calculations. We not only demonstrate the feasibility of growing h-BeO monolayers by MBE, but also illustrate that the large-scale growth, weak substrate interactions, and long-range crystallinity make h-BeO an attractive candidate for future technological applications. More significantly, the ability to create a stable single crystalline atomic sheet without a bulk layered counterpart is an intriguing approach to tailoring novel 2D electronic materials.