This note presents a study of the feasibility of a Free Electron Laser (FEL) using an electron beam from the Compact Linear Collider (CLIC). We first show that, with the nominal CLIC layout, the energy spread at 15 GeV would be too large to allow FEL saturation in an undulator of reasonable length. An alternative scheme was studied, with a dedicated source, with a by-pass of the damping rings and with magnetic compression between the various acceleration stages. With this scheme, the energy spread of the CLIC beam can be reduced from 1.5% to 0.1%, but the emittance is much larger and, although the power gain is better than in the nominal case, FEL saturation is still not reached. We show that the energy spread or the transverse emittance would have to be reduced by another order of magnitude in order to obtain FEL saturation
