  We report on a measurement of the proton structure function $F_2$ in the
range $3.5\times10^{-5}\leq x \leq 4\times10^{-3}$ and 1.5 ${\rm GeV^2} \leq
Q^2 \leq15$ ${\rm GeV^2}$ at the $ep$ collider HERA operating at a
centre-of-mass energy of $\sqrt{s} = 300$ ${\rm GeV}$. The rise of $F_2$ with
decreasing $x$ observed in the previous HERA measurements persists in this
lower $x$ and $Q^2$ range. The $Q^2$ evolution of $F_2$, even at the lowest
$Q^2$ and $x$ measured, is consistent with perturbative QCD.
