  MacMahon proved a simple product formula for the generating function of plane
partitions fitting in a given box. The theorem implies a $q$-enumeration of
lozenge tilings of a semi-regular hexagon on the triangular lattice. In this
paper we generalize MacMahon's classical theorem by $q$-enumerating lozenge
tilings of a new family of hexagons with four adjacent triangles removed from
their boundary.
