  We prove that the KP-I initial-value problem \begin{eqnarray*} \begin{cases}
\partial_tu+\partial_x^3u-\partial_x^{-1}\partial_y^2u+\partial_x(u^2/2)=0
{on}{\R}^2_{x,y}\times {\R}_t; u(x,y,0)=\phi(x,y), \end{cases} \end{eqnarray*}
is locally well-posed in the space \begin{eqnarray*} H^{1,0}(\R^2)=\{\phi\in
L^2(\R^2): \
\norm{\phi}_{H^{1,0}(\R^2)}\approx\norm{\phi}_{L^2}+\norm{\partial_x\phi}_{L^2}<\infty\}.
\end{eqnarray*}
