Predictive numerical simulations of energy conversion systems involving reacting flows are accompanied by high computational cost of solving a system of stiff ordinary differential equations (ODEs) associated with detailed fuel chemistry. This bottleneck becomes more prohibitive for complex hydrocarbon fuels with an increase in the number of reactive species and chemical reactions governing chemical kinetics. In this work, a physics-informed Autoencoder (AE)-neural ODE framework (Phy-ChemNODE) is developed for data-driven modeling of stiff chemical kinetics, wherein a non-linear autoencoder (AE) is employed for dimensionality reduction of the thermochemical state and the NODE learns the temporal evolution of the dynamical system in the latent space obtained from the AE. Both the AE and NODE are trained together in an end-to-end manner. We further enhance the approach by incorporating elemental mass conservationconstraints directly into the loss function during model training. Demonstration studies are performed for methane-oxygen combustion kinetics over a wide range of thermodynamic conditions. Effects of model hyperparameters, such as relative weighting of different terms in the loss function and dimensionality of the AE latent space, are assessed on the accuracy of Phy-ChemNODE. Lastly, a posteriori autoregressive tests show that the proposed data-driven technique achieves an order of magnitude speedup relative to the full methane-oxygen chemical mechanism,while ensuring prediction fidelity and mass conservation.