We investigate the three-body fragmentation of $CH_{3}Cl$ dications induced by intense femtosecond laser pulses in a home-built recoil ion momentum spectrometer setup. This study focuses on two pathways: (1) H + CH + Cl+, and (2) H+ + CH + Cl. To understand the complex excited-state dynamics of the dication and the momentum sharing between the fragments, Dalitz plots, Newton diagrams, and the native frame method were used, which helped to distinguish between the concerted and sequential fragmentation mechanisms. We further discuss the dissociation pathways theoretically using density functional theory calculations. Although the signatures of both concerted and sequential mechanisms were present and overlapping, the concerted mechanism was dominant for both pathways. On positively chirping the pulses, the concerted mechanism remained unaffected, while the sequential mechanism, in some cases, was suppressed. This observation demonstrates that the pulse chirp influences the complex fragmentation dynamics of the $CH_{3}Cl$ dication.