The prospect of realizing entangled quantum states between macroscopic objects and photons has recently stimulated interest in new laser-cooling schemes. For example, laser-cooling of the vibrational modes of a mirror can be achieved by subjecting it to a radiation or photothermal pressure, actively controlled through a servo loop adjusted to oppose its brownian thermal motion within a preset frequency window. In contrast, atoms can be laser-cooled passively without such active feedback, because their random motion is intrinsically damped through their interaction with radiation. Here we report direct experimental evidence for passive (or intrinsic) optical cooling of a micromechanical resonator. We exploit cavity-induced photothermal pressure to quench the brownian vibrational fluctuations of a gold-coated silicon microlever from room temperature down to an effective temperature of 18 K. Extending this method to optical-cavity-induced radiation pressure might enable the quantum limit to be attained, opening the way for experimental investigations of macroscopic quantum superposition states involving numbers of atoms of the order of 10(14).