A new measurement of the proton structure function F2(x, Q2) is reported for momentum transfers squared Q2 between 1.5 GeV2 and 5000 GeV2 and for Bjorken x between 3 · 10-5 and 0.32 using data collected by the HERA experiment H1 in 1994. The data represent an increase in statistics by a factor of ten with respect to the analysis of the 1993 data. Substantial extension of the kinematic range towards low Q2 and x has been achieved using dedicated data samples and events with initial state photon radiation. The structure function is found to increase significantly with decreasing x, even in the lowest accessible Q2 region. The data are well described by a Next to Leading Order QCD fit and the gluon density is extracted.