Simple Summary: The way poultry are fed affects the fatty acid profile of the meat. A sufficient supply of zinc (Zn) is crucial because this element is capable of modulating fatty acid metabolism and can affect the dietary quality of meat. Our study aimed to determine whether Zn glycine chelate used in the diets of Ross 308 broiler chickens can improve the dietary quality of meat due to a beneficial modification of the fatty acid profile. Using statistical methods, we confirmed the effect of the form (sulphate vs. glycine chelate) and/or quantity of Zn used (100% or 50% of the requirement) on the fatty acid profile and dietary quality of thigh meat. However, our results imply that it is sufficient to supply any form of Zn in the amount satisfying 50% of the chicken requirements for Zn to ensure satisfactory dietary quality of their meat. Studies concerning nutritional strategies for the modification of the dietary quality of meat by altering the fatty acid profile are significant to consumers, as such modification can produce good-quality meat for safe consumption without increasing the risk of diet-related civilisational diseases and can even contribute to reducing such a risk. Abstract: The present study aimed to investigate the effect of mineral (sulphate) or organic (glycine chelate) forms of Zn used in quantities covering 100% or 50% of the Zn requirement on the fatty acid profile of the thigh muscles of Ross 308 broiler chickens. We also analysed the dietary value of this meat based on its fatty acid profile. The experimental factors did not influence the content of basic chemical components and the meat’s pH. Although, in terms of statistics, the presented study supports the statement that the form (sulphate vs. glycine chelate) and/or amount of Zn used (100% or 50% of the requirement) affects the fatty acid profile and dietary value of thigh meat, the results imply that the requirement of Ross 308 broiler chickens for Zn was also covered in full when in it was used in amounts covering 50% of the requirement, irrespective of the form in which Zn was used. However, it cannot be explicitly confirmed that the form of Zn affects the analysed parameters of thigh meat.