We prove that the initial value problem associated to a perturbation of the Benjamin-Ono equation or Chen-Lee equation ut + uux + βHuxx + (Hux - uxx) = 0, where x ∈ T, t 0, η 0 and H denotes the usual Hilbert transform, is locally and globally well-posed in the Sobolev spaces Hs(T) for any s - ½. We also prove some ill-posedness issues when s -1.