Aims. A mapping observation of the J = 1/2 Λ-type doubling transition (3.3 GHz) of CH has been conducted toward Heiles Cloud 2 (HCL2) in the Taurus molecular cloud complex to reveal its molecular cloud-scale distribution. Methods. The observations were carried out with the Effelsberg 100 m telescope. Results. The CH emission is found to be extended over the whole region of HCL2. It is brighter in the southeastern part, which encloses the TMC-1 cyanopolyyne peak than in the northwestern part. Its distribution extends continuously from the peak of the neutral carbon emission (CI peak) to the TMC-1 ridge, as if it were connecting the distributions of the [C I] and C 18 O emissions. Since CH is an intermediate in gas-phase chemical reactions from C to CO, its emission should trace the transition region. The above distribution of the CH emission is consistent with this chemical behavior. Since the CH abundance is subject to the chemical evolutionary effect, the CH column density in HCL2 no longer follows a linear correlation wit the H 2 column density reported for diffuse and translucent clouds. More importantly, the CH line profile is found to be composed of the narrow and broad components. Although the broad component is dominant around the CI peak, the narrow component appears in the TMC-1 ridge and dense core regions such as L1527 and TMC-1A. This trend seems to reflect a narrowing of the line width during the formation of dense cores. These results suggest that the 3.3 GHz CH line is a useful tool for tracing the chemical and physical evolution of molecular clouds.