Measurement of the Deep Inelastic Scattering Cross Section at Q^2 ~ 1 GeV^2 with the H1 Experiment --------------------------------------------------------------------------- New data are presented of the inclusive ep scattering cross section in the kinematic region of very low Bjorken x and four-momentum transfer squared Q^2 \sim 1 GeV^2, in the transition region from the non-perturbative to the deep-inelastic domain. The data were taken at HERA in the summer 2000, with a proton beam energy of 920 GeV and an electron beam energy of 27.5 GeV. In a dedicated HERA run, the interaction vertex was shifted by +70 cm, thereby accessing a region of lower Q^2 than at nominal vertex position. With a fourfold increase in statistics and new instrumentation the accuracy of the measurement is improved as compared to previous shifted vertex data. The cross-section measurement is used to obtain new, preliminary data on the proton structure function F_2(x,Q^2), and its rise towards low x is studied.