An efficient method is presented for computing time-varying, component-wise bounds on the solutions of chemical kinetics models subject to an interval of permissible parameters. The model may be any system of ordinary differential equations whose right-hand side may be written as a stoichiometric matrix premultiplying a vector of potentially nonlinear rate functions, and model parameters may include initial conditions, kinetic rate coefficients, controls, disturbances, etc. The method presented differs from other bounding methods in that it takes advantage of the special structure of chemical kinetics models, including known physical bounds and the presence of affine reaction invariants. The method is demonstrated for several case studies, and it is shown that the resulting bounds are nearly always significantly tighter than those computed by a similar method which does not take reaction invariants into account. Finally, the additional computational cost of taking reaction invariants into consideration is negligible.