  We prove that the initial value problem associated to a perturbation of the
Benjamin-Ono equation or Chen-Lee equation $u_t+uu_x+\beta
\mathcal{H}u_{xx}+\eta (\mathcal{H}u_x - u_{xx})=0$, where $x\in \mathbb{T}$,
$t> 0$, $\eta >0$ and $\mathcal{H}$ denotes the usual Hilbert transform, is
locally and globally well-posed in the Sobolev spaces $H^s(\mathbb{T})$ for any
$s>-\frac{1}{2}$. We also prove some ill-posedness issues when $s<-1$.
