Chicken is one of the most widely consumed meats worldwide. The exploration of the bacterial diversity of chicken meat may provide new insights into the chicken-associated microbiome that will lead to moderation of food spoilage or safety. This study was undertaken to explore the bacterial communities of chicken breast and thigh fillets stored at refrigeration (0 °C and 5 °C) and slightly abuse (10 °C) temperatures for 5 days through conventional cultural methods along with next-generation sequencing (NGS) analysis. Total viable counts (TVC), Brochothrix thermosphacta, Pseudomonas spp., and lactic acid bacteria (LAB) were enumerated, while the bacterial communities were mapped through 16S rRNA gene amplicon sequencing. Chicken breast and thigh fillets possessed a complex bacterial structure that incorporated a total of >200 Operational Taxonomic Units (OTUs) at the genus level. The core microbiota of fresh samples consisted of Acinetobacter, Brochothrix, Flavobacterium, Pseudomonas, Psychrobacter, and Vibrionaceae (family). These genera persisted until the end of storage in >80% of samples, except Psychrobacter and Flavobacterium, while Photobacterium was also identified. Hierarchical clustering showed a distinction of samples based on storage time and chicken part. Conventional plate counting with growth media commonly used in spoilage studies did not always correspond to the microbial community profiles derived from NGS analysis, especially in Pseudomonas, Acinetobacter, Photobacterium, and Vibrionaceae. Results of the present study highlight Photobacterium and Vibrionaceae, in general, as potent chicken meat spoilers and suggest the necessity to combine classical microbiological methods along with NGS technologies to characterize chicken meat spoilage microbiota.