We report the direct observation of a novel type of rainbow caustic. In contrast to known examples, this caustic originates from a dissipative, stochastic process. We have observed this using cold 87 Rb atoms bouncing inelastically on an evanescent-wave atom mirror. The caustic appears as a sharp peak at the lower edge of the asymmetric velocity distribution of the bouncing atoms. The stochastic process is a spontaneous Raman transition due to photon scattering during the bounce. The results are in good agreement with a classical calculation.32.80. Lg, 42.50.Vk, Caustics are ubiquitous phenomena in nature. Examples are the cusp-shaped patterns of light reflection on the inside of a coffee-cup and the patterns of bright lines observed on the bottom of a swimming pool [1]. The prime example of a caustic is the common rainbow, which can be understood in a ray-optics picture by considering how the scattering angle of a light ray depends on its impact parameter on a water droplet [2] . Whereas the incident rays have smoothly distributed impact parameters, the outgoing rays pile up where the scattering angle has a local extremum. Such a divergence of the ray density, the caustic, appears at the rainbow angle. In atomic [3] and nuclear [4] scattering experiments analogous rainbow phenomena have also been observed.The examples of caustics that have been known so far have in common that the outgoing parameter (scattering angle) is a deterministic function of the incoming parameter (impact parameter). In this Letter we report on our observation of a new type of rainbow caustic existing by virtue of a stochastic process, which distributes a singlevalued "impact parameter" over a range of "scattering angles". To our knowledge, such stochastic caustics have not been observed before.We have observed this caustic in the vertical velocity distribution of cold atoms, after bouncing inelastically off an evanescent-wave mirror [5][6][7][8]. Previous experiments on the transverse velocity distribution of atoms bouncing elastically on corrugated mirrors [9,10] also allow an interpretation in terms of caustics. However, those were of the usual deterministic kind, where the outgoing transverse velocity is a deterministic function of the position where the atom hits the mirror. The caustic then originates from atoms reflecting from inflection points on the mirror surface.Whereas other experiments on inelastically bouncing atoms concentrated on the cooling properties, the appearence of the velocity caustic seems to have escaped attention. The incident atoms in our experiment are nearly monochromatic, i.e. they have a narrow velocity distribution ∆v/v = 0.03. During the bounce the atoms are optically pumped to a different hyperfine groundstate, by a spontaneous Raman transition. They leave the surface with less kinetic energy, due to the difference in optical potential. The outgoing atoms have a broad velocity distribution. This is due to the stochastic nature of the spontaneous Raman process, so that atoms make the transition at differe...