We present the first observation of a long-lived valence state of H-2
close to the ionization threshold, populated in a double resonance las
er excitation scheme with extreme ultraviolet radiation in the first s
tep. Level energies of rovibrational states, confined in the outer par
t of the double-well <H(H)over bar (1)>Sigma(g)(+) potential at a larg
e internuclear distance of 11 a.u., have been determined with an accur
acy of 0.04 cm(-1). Observed weak autoionization, increasing with vibr
ational energy, is explained by tunneling through the potential barrie
r.