Poultry manure is the main source of agricultural and rural non-point source pollution, and its effective disposal through anaerobic digestion (AD) is of great significance; meanwhile, the high nitrogen content of chicken manure makes it a typical feedstock for anaerobic digestion. The performance of chicken-manure-based AD at gradient organic loading rates (OLRs) in a continuous stirred tank reactor (CSTR) was investigated herein. The whole AD process was divided into five stages according to different OLRs, and it lasted for 150 days. The results showed that the biogas yield increased with increasing OLR, which was based on the volatile solids (VS), before reaching up to 11.5 g VS/(L·d), while the methane content was kept relatively stable and maintained at approximately 60%. However, when the VS was further increased to 11.5 g VS/(L·d), the total ammonia nitrogen (TAN), pH, and alkalinity (CaCO3) rose to 2560 mg·L−1, 8.2, and 15,000 mg·L−1, respectively, while the volumetric biogas production rate (VBPR), methane content, and VS removal efficiency decreased to 0.30 L·(L·d)−1, 45%, and 40%, respectively. Therefore, the AD performance immediately deteriorated and ammonia inhibition occurred. Further analysis demonstrated that the microbial biomass yield and concentrations dropped dramatically in this period. These results indicated that the AD stayed steady when the OLR was lower than 11.5 g VS/(L·d); this also provides valuable information for improving the efficiency and stability of AD of a nitrogen-rich substrate.