We describe in this paper a new beam profile monitor which is suitable for a low-emittance circulating electron beam. The monitor, termed as a laser wire profile monitor, utilizes a CW laser and an optical cavity to minimize interference with an electron beam. A laser beam with a very thin waist is realized by employing the cavity of nearly concentric mirror configuration while the intensity is amplified by adjusting the cavity length to a Fabry-Perot resonance condition. We have built and tested a prototype cavity. It is found that a beam waist of 12 μm and an effective power of 3300 mW were achieved in the laser wire with good long-term stability. It will be installed in the ATF damping ring at KEK, in which a transverse electron beam size of about 10 μm is expected.