A theory for polarized absorption in crystalline oligoacenes is presented, which includes Frenkel exciton coupling, the coupling between Frenkel and charge-transfer (CT) excitons, and the coupling of all neutral and ionic excited states to the dominant ring-breathing vibrational mode. For tetracene, spectra calculated using all Frenkel couplings among the five lowest energy molecular singlet states predict a Davydov splitting (DS) of the lowest energy (0-0) vibronic band of only -32 cm(-1), far smaller than the measured value of 631 cm(-1) and of the wrong sign-a negative sign indicating that the polarizations of the lower and upper Davydov components are reversed from experiment. Inclusion of Frenkel-CT coupling dramatically improves the agreement with experiment, yielding a 0-0 DS of 601 cm(-1) and a nearly quantitative reproduction of the relative spectral intensities of the 0-n vibronic components. Our analysis also shows that CT mixing increases with the size of the oligoacenes. We discuss the implications of these results on exciton dissociation and transport.