In this letter, we report on the structural and transport measurements of ultrathin MgB2 films grown by hybrid physical-chemical vapor deposition followed by low incident angle Ar ion milling. The ultrathin films as thin as 1.8 nm, or 6 unit cells, exhibit excellent superconducting properties such as high critical temperature (Tc) and high critical current density (Jc). The results show the great potential of these ultrathin films for superconducting devices and present a possibility to explore superconductivity in MgB2 at the 2D limit.