Anomalously broad diffuse interstellar bands (DIBs) at 5780.5, 5797.1, 6196.0, and 6613.6 A are found in absorption along the line of sight to Herschel 36, the star illuminating the bright Hourglass region of the H II region Messier 8. Interstellar absorption from excited CH+ in the J=1 level and from excited CH in the J=3/2 level is also seen. To our knowledge, neither those excited molecular lines nor such strongly extended DIBs have previously been seen in absorption from interstellar gas. These unusual features appear to arise in a small region near Herschel 36 which contains most of the neutral interstellar material in the sight line. The CH+ and CH in that region are radiatively excited by strong far-IR radiation from the adjacent infrared source Her 36 SE. Similarly, the broadening of the DIBs toward Herschel 36 may be due to radiative pumping of closely spaced high-J rotational levels of relatively small, polar carrier molecules. If this picture of excited rotational states for the DIB carriers is correct and applicable to most DIBs, the 2.7 degree cosmic microwave background may set the minimum widths (about 0.35 A) of known DIBs, with molecular processes and/or local radiation fields producing the larger widths found for the broader DIBs. Despite the intense local UV radiation field within the cluster NGC 6530, no previously undetected DIBs stronger than 10 mA in equivalent width are found in the optical spectrum of Herschel 36, suggesting that neither dissociation nor ionization of the carriers of the known DIBs by this intense field creates new carriers with easily detectable DIB-like features. Possibly related profile anomalies for several other DIBs are noted.