We present the machine parameters and physics capabilities of the CLIC Higgs Experiment (CLICHE), a low-energy γγ collider based on CLIC 1, the demonstration project for the higher-energy two-beam accelerator CLIC. CLICHE is conceived as a factory capable of producing around 20,000 light Higgs bosons per year. We discuss the requirements for the CLIC 1 beams and a laser backscattering system capable of producing a γγ total (peak) luminosity of 2.0 (0.36) × 10 34 cm −2 s −1 with E CM (γγ) ∼ 115 GeV. We show how CLICHE could be used to measure accurately the mass, bb, W W and γγ decays of a light Higgs boson. We illustrate how these measurements may distinguish between the Standard Model Higgs boson and those in supersymmetric and more general two-Higgs-doublet models, complementing the measurements to be made with other accelerators. We also comment on other prospects in γγ and e − γ physics with CLICHE.