Chemical compositions of exoplanets can provide key insights into their physical processes, and formation and evolutionary histories. Atmospheric spectroscopy provides a direct avenue to probe exoplanetary compositions. However, whether obtained in transit or thermal emission, spectroscopic observations probe limited pressure windows of planetary atmospheres and are directly sensitive to only a limited set of spectroscopically active species. It is therefore critical to have chemical models that can relate retrieved atmospheric compositions to an atmosphere's bulk physical and chemical state. To this end we present LEVI, a new chemical kinetics code for modelling exoplanetary atmospheres. LEVI calculates the gas phase hydrogen, oxygen, carbon, and nitrogen chemistry in planetary atmospheres. Here we focus on hot gas giants. Applying LEVI, we investigate how variations in bulk C/O and N/O affects the observable atmospheric chemistry in hot Jupiters. For typical hot Jupiters we demonstrate the strong sensitivity of molecular detections to the atmospheric C/O. Molecular detections are conversely less sensitive to the atmospheric N/O ratio, although highly super-solar N/O can decrease the C/O required for HCN and NH3 detection. Using a new P-T profile for HD 209458b without a thermal inversion, we evaluate recently reported detection's of CO, H2O and HCN in its day-side atmosphere. We find that our models are consistent with the detected species, albeit with a narrow compositional window around C/O $\sim$ 1. A C/O $\gtrsim$ 0.9 (1.6 times solar) was required to meet the minimum reported value for HCN, while a C/O $\lesssim$ 1 (1.8 times solar) was required to fit the nominal H2O abundance.