  Using 2.93 fb$^{-1}$ of $e^+e^-$ collision data taken with the BESIII
detector at a center-of-mass energy of 3.773 $\rm \,GeV$, the observation of
the $D^0\to K_1(1270)^- e^+\nu_e$ semileptonic decay is presented. The
statistical significance of the decay $D^0\to K_1(1270)^- e^+\nu_e$ is greater
than $10\sigma$. The branching fraction of $D^0\to K_1(1270)^- e^+\nu_e$ is
measured to be $(1.09\pm0.13^{+0.09}_{-0.16} \pm 0.12)\times10^{-3}$. Here, the
first uncertainty is statistical, the second is systematic, and the third
originates from the assumed branching fraction of $K_1(1270)^- \rightarrow
K^-\pi^+\pi^-$. The fraction of longitudinal polarization in $D^0\to
K_1(1270)^- e^+\nu_e$ is determined for the first time to be $0.50\pm0.19_{\rm
stat}\pm0.08_{\rm syst}$.
