Inferences of molecular compositions of exoplanetary atmospheres have generally focused on C, H, and O-bearing molecules. Recently, additional absorption in HST WFC3 transmission spectra around 1.55$\mu$m has been attributed to nitrogen-bearing chemical species: NH$3$ or HCN. These species, if present in significant abundance, would be strong indicators of disequilibrium chemical processes -- e.g. vertical mixing and photochemistry. The derived N abundance, in turn, could also place important constraints on planetary formation mechanisms. Here, we examine the detectability of nitrogen chemistry in exoplanetary atmospheres. In addition to the WFC3 bandpass (1.1-1.7$\mu$m), we find that observations in K-band at $\sim$2.2$\mu$m,achievablewithpresentground-basedtelescopes,sampleastrongNH$_3$ feature, whilst observations at $\sim$3.1$\mu$m and $\sim$4.0$\mu$msamplestrongHCNfeatures.Inanticipationofsuchobservations,wepredictabsorptionfeatureamplitudesduetonitrogenchemistryinthe1-5$\mu$mspectralrangepossibleforatypicalhotJupiter.Finally,weconductatmosphericretrievalsof9hotJupitertransmissionspectrainsearchofnear-infraredabsorptionfeaturessuggestiveofnitrogenchemistry.WereportweakdetectionsofNH$_3$ in WASP-31b (2.2$\sigma$), HCN in WASP-63b (2.3$\sigma$), and excess absorption that could be attributed to NH$3$ in HD 209458b. High-precision observations from 1-5$\mu$m (e.g., with the James Webb Space Telescope), will enable definitive detections of nitrogen chemistry, in turn serving as powerful diagnostics of disequilibrium atmospheric chemistry and planetary formation processes.