Type I and II halogen bonds are well-recognized motifs that commonly occur within crystals. Quantum calculations are applied to examine whether such geometries might occur in their closely related chalcogen bond cousins. Homodimers are constructed of the R1R2C=Y and R1R2Y monomers, wherein Y represents a chalcogen atom, S, Se, or Te; R1 and R2 refer to either H or F. A Type II (T2) geometry wherein the lone pair of one Y is closely aligned with a σ-hole of its partner represents a stable arrangement for all except YH2, although not all such structures are true minima. The symmetric T1 geometry in which each Y atom serves as both electron donor and acceptor in the chalcogen bond is slightly higher in energy for R1R2C=Y, but the reverse is true for R1R2Y. Due to their deeper σ-holes, the latter molecules engage in stronger chalcogen bonds than do the former, with the exception of H2Y, whose dimers are barely bound. The interaction energies rise as the Y atom grows larger: S < Se < Te.