We introduce the Calogero-Moser derivative nonlinear Schrödinger equation. We study its semiclassical limit by establishing the existence of a weak limit solution when we neglect the dispersion part of the equation. This weak limit solution will be identified explicitly. In a subsequent step, we explore the relationship between this weak limit and the branches of the multivalued solution of the Burgers equation. Finally, we derive a maximal principle that governs this weak limit solution