Evidence is presented using data taken with the H1 detector at HERA for a class of deep inelastic electron-proton scattering (DIS) events (5 < Q2 < 120 GeV2) at low Bjorken-x (10-4 < x < 10-2) which have almost no hadronic energy flow in a large interval of pseudo-rapidity around the proton remnant direction and which cannot be attributed to our present understanding of DIS and fluctuations in final state hadronic fragmentation. From an integrated luminosity of 273 nb-1, 734 events, that is about 5% of the total DIS sample, have no energy deposition greater than 400 MeV forward of laboratory pseudo-rapidity ηmax = 1.8 up to the largest measurable pseudo-rapidity of about 3.65. Evidence that about 10% of observed rapidity gap events are exclusive vector meson electroproduction is presented. Good descriptions of the data are obtained using models based either on a vector meson dominance like picture, which includes a large fraction of inelastic virtual photon dissociation, or on deep inelastic electron-pomeron scattering in which the partonic sub-structure of the latter is resolved. © 1994.