Significant efforts made by the gas turbine industry have helped reduce nitrogen oxides (NOx) emissions considerably. To meet and surpass the increasingly stringent regulations, accurate and robust thermochemical mechanisms are needed to help design future sub-10 ppm combustion systems. Uncertainty in kinetic modeling, however, can result in large prediction uncertainty and significant discrepancy between models that hinder the identification of promising combustors with confidence. Direct reaction rate measurements are seldom available for some reactions, especially when involving short-lived radicals such as methylidyne, CH. As the main precursor to the prompt-NO formation pathway, its large parametric uncertainty directly propagates through the nitrogen chemistry preventing accurate and precise emissions predictions. Recent independent CH concentration measurements obtained at various operating conditions are used as indirect rate measurements to perform statistical, or Bayesian, calibration. A subset of important reactions in the CH chemistry affecting peak-CH concentration is identified through uncertainty-weighted sensitivity analysis to first constrain the parametric space of this prompt-NO precursor. Spectral expansion provides the surrogate model used in the Markov-Chain Monte Carlo method to evaluate the posterior kinetic distribution. The resulting constrained CH-chemistry better captures experimental measurements while providing smaller prediction uncertainty of a similar order as the uncertainty of the measurements, which can increase the confidence in simulation results to identify promising future low-emissions configurations. For the quasi-steady-state species CH, fuel decomposition reactions leading to CH production are constrained while little impact is observed for intermediate reactions within the CH-chemistry. The reduction in prediction uncertainty results mainly from the constrained correlations between parameters which greatly limit the set of feasible reaction rate combinations. Additional independent direct and indirect measurements would be necessary to further constrain rate parameters in the CH chemistry, but this calibration demonstrates that predictions of radical species can be improved by assimilating enough data.