Calculations of the lowest triplet state potential energy surface for the C(P-3) + CH4 reaction have been performed using the CCSD(T)/6-311+G(3df,2p)//QCISD/6-311G(d,p) method, and the microcanonical RRKM approach has been used to compute rate constants for individual reaction steps and product branching ratios. The results show that the reaction can occur by abstraction and insertion mechanisms. The abstraction pathway producing CH((2)Pi) + CH3((2)A(2)") has a barrier of 26.9 kcal/mol relative to the reactants. The insertion leading to the HC-CH3((3)A") intermediate via a 12.2 kcal/mol barrier followed by its isomerization to H2C-CH2-((3)A(1)) (through a 1,2 H shift) and/or by dissociation with an H-atom loss is found to be a more favorable mechanism. At a low excess internal energy originating from the collision energy (12.2 kcal/mol), the sole reaction products are C2H3 + H, where 90% of them are formed through the fragmentation of HC-CH3 and the rest (10%) are produced via the H2C-CH2 intermediate. At the higher excess internal energy (2 eV), CH + CH3 can be formed mainly through the H-abstraction channel. The calculated C2H3 + H and CH + CH3 branching ratios at the excess internal energy of 2 eV are 69.8 and 30.2%, respectively. With further increases of the excess internal energy, the abstraction channel becomes more important, and the CH + CH3 branching ratio increases to 68.9 and 82.8% at 3 and 4 eV, respectively. The C2H2 + H-2 products can be formed only through the secondary C2H3 + H hydrogen disproportionation reactions or via singlet-triplet intersystem crossing in the vicinity of the HC-CH3 intermediate followed by fragmentation of the vibrationally hot ground-state singlet C2H4 molecule. Since only the CH + CH3 products have been characterized so far experimentally, 9 new experimental measurements are encouraged.