Thermal emission spectra of exoplanets provide constraints on the chemical compositions, pressure-temperature (P-T) profiles, and energy transport in exoplanetary atmospheres. Accurate inferences of these properties rely on the robustness of the atmospheric retrieval methods employed. While extant retrieval codes have provided significant constraints on molecular abundances and temperature profiles in several exoplanetary atmospheres, the constraints on their deviations from thermal and chemical equilibria have yet to be fully explored. Our present work is a step in this direction. We report HyDRA, a disequilibrium retrieval framework for thermal emission spectra of exoplanetary atmospheres. The retrieval code uses the standard architecture of a parametric atmospheric model coupled with Bayesian statistical inference using the Nested Sampling algorithm. For a given dataset, the retrieved compositions and P-T profiles are used in tandem with the GENESIS self-consistent atmospheric model to constrain layer-by-layer deviations from chemical and radiative-convective equilibrium in the observable atmosphere. We demonstrate HyDRA on the Hot Jupiter WASP-43b with a high-precision emission spectrum. We retrieve an H2O mixing ratio of log(H2O) = -3.54^{+0.82}_{-0.52}, consistent with previous studies. We detect H2O and a combined CO/CO2 at 8-sigma significance. We find the dayside P-T profile to be consistent with radiative-convective equilibrium within the 1-sigma limits and with low day-night redistribution, consistent with previous studies. The derived compositions are also consistent with thermochemical equilibrium for the corresponding distribution of P-T profiles. In the era of high precision and high resolution emission spectroscopy, HyDRA provides a path to retrieve disequilibrium phenomena in exoplanetary atmospheres.