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New observations of 16 dwarf elliptical galaxies in the Virgo Clusterindicate that at least seven dEs have significant velocity gradients alongtheir optical major axis, with typical rotation amplitudes of 20-30 km/s. Ofthe remaining nine galaxies in this sample, 6 have velocity gradients less than20 km/s kpc^{-1} while the other 3 observations had too low of asignal--to--noise ratio to determine an accurate velocity gradient. Typicalvelocity dispersions for these galaxies are ~44 +/- 5 km/s, indicating thatrotation can be a significant component of the stellar dynamics of Virgo dEs.When corrected for the limited spatial extent of the spectral data, therotation amplitudes of the rotating dEs are comparable to those of similarbrightness dIs. Evidence for a relationship between the rotation amplitude andgalaxy luminosity is found, and, in fact, agrees well with the Tully-Fisherrelation. The similarity in the scaling relations of dIs and dEs implies thatit is unlikely that dEs evolve from significantly more luminous galaxies. Theseobservations reaffirm the possibility that some cluster dwarf ellipticalgalaxies may be formed when the neutral gaseous medium is stripped from dwarfirregular galaxies in the cluster environment. We hypothesize that severaldifferent mechanisms are involved in the creation of the overall population ofdE galaxies, and that stripping of infalling dIs may be the dominant process inthe creation of dEs in clusters like Virgo.Comment: 33 pages, 8 figures (1 color). Published in A

Rotationally Supported Virgo Cluster Dwarf Elliptical Galaxies: Stripped Dwarf Irregular Galaxies?