Flow-controlled fingering of the liquid expanded/liquid condensed phase boundary in a 2-d insoluble monolayer is investigated using a laser-induced thermocapillary pump. Spatially periodic perturbations of the initially smooth monolayer phase boundary between a liquid expanded and liquid condensed phase are shown to lead to the development of steady profile of one-dimensional fingers. The steady-state modulation wave vector and the transient growth rate increase with the flow velocity that drives the instability following power scaling laws consistent with a theory of Bruinsma, Rondelez, and Levine (Bruinsma, R.; Rondelez, F.; Levine, A. Eur. Phys. J. E. 2001, 6, 191) on flow rather than diffusion dominated instabilities in monolayers.