We measure absolute methylidyne (CH) radical concentrations in a series of rich 31.0 Torr (4.13 kPa) methane-oxygen-argon flames using cavity ringdown spectroscopy. Probing via the CH A(2)Delta-X(2)Pi transition near 430 nm gives a sensitivity of 3 x 10(9) cm(-3) for our experimental conditions, yielding a signal-to-noise ratio greater than 1000 for the strongest transitions observed. We measure profiles of CH mole fraction as a function of height above a flat-flame burner for rich flames with equivalence ratios of 1.0, 1.2, 1.4, and 1.6. These flames are modeled using the following mechanisms: (1) the GRI Mech 2.11, (2) a mechanism by Prada and Miller, (3) a modified GRI2.11 mechanism, which employs a more realistic increased CH + O-2 rate coefficient, and (4) the new GRI Mech 3.0. Generally good agreement between the models and the data is found, with the GRI 3.0 and modified 2.11 mechanisms best reproducing the data. The greatest discrepancies are observed at the richest stoichiometry, where all of the models predict a wider CH profile shifted further from the burner than experimentally observed.