The primary objective of this study was to investigate the impact of a phytogenic additive (PA) in broiler chickens’ diet on production, physiochemical parameters, and the profile of volatile organic compounds present in broiler chickens’ meat. The experiment was conducted in a commercial chicken house, where Ross 308 broiler chickens were divided into two groups, each consisting of 65,000 broilers. One group was fed a diet supplemented with 100 ppm of PA throughout the rearing period. The primary chemical composition of the meat and its physicochemical parameters were determined. A visual assessment of breast muscles for defects and volatile organic compounds were evaluated using an electronic nose system. No statistically significant differences were shown in the production performance of the chickens; while summarizing all production parameters, a higher EPEF index of 31 points in the experimental group was highlighted. Breast muscle quality showed differences in drip loss and WHC (p ≤ 0.01) in favor of the experimental group, and a lower cutting force value (p ≤ 0.05) was found for breast muscles from the experimental group. The group also had a lower proportion of muscles with a white striping defect, and the results of volatile organic compound profiling showed the most aroma units.