The readily accessible rhodium(I) complex [Rh(CNC–Me)(SOMe2)][BArF4], featuring a NHC-based pincer ligand, is shown to undergo selective oxidative addition of the C–C bond of biphenylene and the C–Cl bond of chlorobenzene under mild conditions. The synthesis and organometallic chemistry of rhodium(I) complex [Rh(CNC–Me)(SOMe2)][BArF4], featuring NHC-based pincer and labile dimethyl sulfoxide ligands, is reported. This complex reacts with biphenylene and chlorobenzene to afford products resulting from selective C–C and C–Cl bond activation, [Rh(CNC–Me)(2,2'-biphenyl)(OSMe2)][BArF4] and [Rh(CNC–Me)(Ph)Cl(OSMe2)][BArF4], respectively. A detailed DFT-based computational analysis indicates that C–H bond oxidative addition of these substrates is kinetically competitive, but in all cases endergonic: contrasting the large thermodynamic driving force calculated for insertion of the metal into the C–C and C–Cl bonds, respectively. Under equivalent conditions the substrates are not activated by the phosphine-based pincer complex [Rh(PNP-iPr)(SOMe2)][BArF4].