  The eclipsing binary DI Herculis garnered interest for several decades
because of an apparent disagreement between the observed and calculated values
of the apsidal precession rate. The problem was resolved when both stars were
found to have high obliquities, but the reason for the high obliquities is
unknown. Here we investigate the possibility that the obliquities are (or were)
excited by an unseen tertiary star. Obliquity excitation in the current orbital
configuration can be ruled out with existing data; any tertiary star that is
sufficiently close or massive to overcome the strong spin-orbit coupling of the
binary would have been detected through various dynamical effects. It remains
possible that the orbit of DI Herculis was initially wider and the obliquity
was excited during high-eccentricity tidal migration driven by a tertiary
companion, but in this scenario it would be difficult to explain why the
observed spin rates are much faster than the pseudo-synchronous rate. In
addition, inward migration is most likely to arise when the mass of the
perturbing star is comparable to the binary mass, and such a bright tertiary
would have been detected in imaging or spectroscopic data. Alternative
explanations that do not invoke a tertiary star should be sought for the large
obliquities in DI Herculis.
