We investigate scalar-field theories with a field-dependent coupling to matter and show the existence of a chameleon mechanism. The thin-shell solutions for a spherical body are found, and used to investigate the consequences for the Eöt-Wash experiment, fifth-force searches and Casimir force experiments. Requiring that the scalar-field evades gravitational tests, we find that the coupling is sensitive to a mass-scale which is of order of the Hubble scale today. The background evolution is found to agree with LDCM, but the linear matter perturbations will, for some values of the parameters exhibit a scale dependent growth which may allow future experiments of the large scale structure to discriminate our models from LCDM. However, for this to be the case, local gravity bounds require that the scalar-field couples to dark matter only.