The Spitzer spectrum of the giant FR II radio galaxy 3C 326 is dominated by very strong molecular hydrogen emission lines on a faint IR continuum. The H2 emission originates in the northern component of a double-galaxy system associated with 3C 326. The integrated luminosity in H2 pure-rotational lines is 8.0E41 erg/s, which corresponds to 17% of the 8-70 micron luminosity of the galaxy. A wide range of temperatures (125-1000 K) is measured from the H2 0-0 S(0)-S(7) transitions, leading to a warm H2 mass of 1.1E9 Msun. Low-excitation ionic forbidden emission lines are consistent with an optical LINER classification for the active nucleus, which is not luminous enough to power the observed H2 emission. The H2 could be shock-heated by the radio jets, but there is no direct indication of this. More likely, the H2 is shock-heated in a tidal accretion flow induced by interaction with the southern companion galaxy. The latter scenario is supported by an irregular morphology, tidal bridge, and possible tidal tail imaged with IRAC at 3-9 micron. Unlike ULIRGs, which in some cases exhibit H2 line luminosities of comparable strength, 3C 326 shows little star-formation activity (~0.1 Msun/yr). This may represent an important stage in galaxy evolution. Starburst activity and efficient accretion onto the central supermassive black hole may be delayed until the shock-heated H2 can kinematically settle and cool