The first of a new class of doubly excited valence states of van der Waals molecules, Mg(3p pi,3p pi(3)P(J)). Ar((3) Sigma(-)), has been discovered anti characterized by resonance two-photon ionization spectroscopy. This state has been found to be quite strongly bound (D-0=2850 +/- 100 cm(-1) and to have a very short bond length (R(0)=2.41+/-0.02 Angstrom). The analogous singly excited state, Mg(3s3p pi(3)P(J)) . Ar((3) Pi(0-)), in stark contrast, has a very much smaller bond strength (D-0=160+/-40 cm(-1)) and a longer bond length (R(0)=3.66+/-0.02 Angstrom). In fact, the new Mg(3p pi 3p pi(3)P(J)). Ar state is more than twice as bound than even the Mg(3s S-2(1/2)). Ar+ ground-state ion (D-0=1240+/-40 cm(-1), R(0)=2.82 Angstrom). The strong bonding is due both to the transverse alignment of the Mg(3p pi) electrons and particularly to the lack of a Mg(3s) electron. The resulting loss of Mg(3s sigma)/Ar(3p sigma)(2) repulsive forces facilitates close approach of the Ar atom. This is turn allows attractive Mg(3p pi)(2)/Ar dispersive forces and Mg2+/Ar ion/induced-dipole type forces to continue to much smaller internuclear distances, coating a strong, short van der Waals bond. Possible mechanisms for the parity-dependent predissociation and the apparent "spin-spin" type splittings observed for the Mg(3p pi,3p pi(3)p(J)). Ar((3) Sigma(-)) State are also discussed.