  This paper is concerned with a one dimensional (1D) derivative nonlinear
Schr\"odinger equation with periodic boundary conditions \begin{equation*}
  \mi u_t+u_{xx}+\mi |u|^2u_x=0, \ \ x\in
\mathbb{T}:=\mathbb{R}/2\pi\mathbb{Z}. \end{equation*} We show that above
equation admits a family of real analytic quasi-periodic solutions with two
Diophantine frequencies. The proof is based on a partial Birkhoff normal form
and KAM method.
