Motivated by the work of Cooper & Showman, we revisit the chemical relaxation method, which seeks to enhance the computational efficiency of chemical-kinetics calculations by replacing the chemical network with a handful of independent source/sink terms. Chemical relaxation solves the evolution of the system and can treat disequilibrium chemistry, as the source/sink terms are driven towards chemical equilibrium on a prescribed chemical timescale, but it has surprisingly never been validated. First, we generalize the treatment by forgoing the use of a single chemical timescale, instead developing a pathway analysis tool that allows us to identify the rate-limiting reaction as a function of temperature and pressure. For the interconversion between methane and carbon monoxide and between ammonia, and molecular nitrogen, we identify the key rate-limiting reactions for conditions relevant to currently characterizable exo-atmospheres (500-3000 K, 0.1 mbar to 1 kbar). Second, we extend chemical relaxation to include carbon dioxide and water. Third, we examine the role of metallicity and carbon-to-oxygen ratio in chemical relaxation. Fourth, we apply our pathway analysis tool to diagnose the differences between our chemical network and that of Moses and Venot. Finally, we validate the chemical relaxation method against full chemical kinetics calculations in one dimension. For WASP-18b-, HD 189733b- and GJ 1214-b-like atmospheres, we show that chemical relaxation is mostly accurate to within an order of magnitude, a factor of 2 and $\sim 10\%$, respectively. The level of accuracy attained allows for the chemical relaxation method to be included in three-dimensional general circulation models.