An unusual quasi-two-dimensional heavy band mass van Hove singularity (vHs) lies very near the Fermi energy in MgCNi₃, recently reported to superconduct at 8.5 K. This compound is strongly exchange enhanced and is unstable to ferromagnetism upon hole doping with 12% Mg → Na or Li. The 1/4-depleted fcc (frustrated) Ni sublattice and lack of Fermi surface nesting argues against competing antiferromagnetic and charge density wave instabilities. We identify an essentially infinite mass along the M-Γ line, leading to quasi-two-dimensionality of this vHs may promote unconventional p-wave pairing that could coexist with superconductivity.