We use Green Bank Ammonia Survey observations of NH$_3$ (1,1) and (2,2) emission with 32 FWHM resolution from a ~ 10 pc$^{2}$ portion of the Cepheus-L1251 molecular cloud to identify hierarchical dense gas structures. Our dendrogram analysis of the NH$_3$ data results in 22 top-level structures, which reside within 13 lower-level, parent structures. The structures are compact (0.01 pc $lesssim R_{eff} lesssim$ 0.1 pc) and are spatially correlated with the highest H$_2$ column density portions of the cloud. We also compare the ammonia data to a catalog of dense cores identified by higher-resolution (18.2 FWHM) Herschel Space Observatory observations of dust continuum emission from Cepheus-L1251. Maps of kinetic gas temperature, velocity dispersion, and NH$_3$ column density, derived from detailed modeling of the NH$_3$ data, are used to investigate the stability and chemistry of the ammonia-identified and Herschel-identified structures. We show that the dust and dense gas in the structures have similar temperatures, with median $T_{dust}$ and $T_K$ measurements of 11.7 $pm$ 1.1 K and 10.3 $pm$ 2.0 K, respectively. Based on a virial analysis, we find that the ammonia-identified structures are gravitationally dominated, yet may be in or near a state of virial equilibrium. Meanwhile, the majority of the Herschel-identified dense cores appear to be not bound by their own gravity and instead confined by external pressure. CCS $(2_0-1_0)$ and HC$_5$N $(9-8)$ emission from the region reveal broader line widths and centroid velocity offsets when compared to the NH$_3$ (1,1) emission in some cases, likely due to these carbon-based molecules tracing the turbulent outer layers of the dense cores.
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