We describe a new type of beam profile monitor developed for measurements of an electron beam as small as 10 gin in size.. This monitor is based on the Compton scattering of electrons with a laser light target. A thin and intense laser beam (laser wire) is produced by injecting a CW laser beam into a Fabry-Perot optical cavity. We were able to obtain a stable laser wire having a beam waist of 14.52 +/- 0.55 mum and a power gain of 220 +/- 20. This monitor was installed in the ATF damping ring at KEK, and was used to measure its vertical emittance. We report in this paper the development and performance studies of this monitor in detail.