The present study discusses the technofunctional properties (color, texture) of grilled chicken with both objective (colorimeter, texture profile) analysis and subjective (sensory) analysis. Besides them, the total content of potentially carcinogenic heterocyclic amines (HCAs) was also monitored by the applied grilling time–temperature combinations. The same samples were analyzed during the heat treatment of chicken breast samples for 5–15 min at 150–230 °C on an electric contact grill. The grilling variables included the effect of skin cover. Among the structural parameters, hardness exhibited a significant difference between the groups of skin-covered and not-covered ones, and in this case, a linear connection was also found with the time and temperature values, respectively. The structural parameters obtained by sensory and instrumental analysis were compared to each other. In addition, the structural parameters were compared to the color ones (sensory, color according to the CIELAB system: brightness, redness, and yellowness) and to the total HCA content. In the case of closed grilling, sensory-evaluated parameters such as juiciness and tenderness showed a strong negative correlation to instrumentally measured hardness (R = −0.879; −0.749) and chewiness (R = −0.872; −0.718) due to the water loss from the increase in grilling temperature and time. The total HCA content positively correlated to chewiness (R = 0.789). The sensory color parameter and the brightness had a strong connection with juiciness (R = 0.738; 0.723), hardness (R = −0.795; −0.706), and chewiness (R = −0.843; −0.818); redness showed positive correlation to cohesiveness (R = 0.764) and chewiness (R = 0.829). Accordingly, juiciness and chewiness showed a connection to the total HCA levels, which makes it possible to carry out further research on instrumental and sensory parameters that may predict the formation of hazardous amounts of carcinogenic heterocyclic amines.