Chickpea is a highly nutritious pulse crop with low digestible carbohydrates (40–60%), protein (15–22%), essential fats (4–8%), and a range of minerals and vitamins. The fatty acid composition of the seed adds value because fats govern the texture, shelf-life, flavor, aroma, and nutritional composition of chickpea-based food products. Therefore, the biofortification of essential fatty acids has become a nutritional breeding target for chickpea crop improvement programs worldwide. This paper examines global chickpea production, focusing on plant lipids, their functions, and their benefits to human health. In addition, this paper also reviews the chemical analysis of essential fatty acids and possible breeding targets to enrich essential fatty acids in chickpea (Cicer arietinum) biofortification. Biofortification of chickpea for essential fatty acids within safe levels will improve human health and support food processing to retain the quality and flavor of chickpea-based food products. Essential fatty acid biofortification is possible by phenotyping diverse chickpea germplasm over suitable locations and years and identifying the candidate genes responsible for quantitative trait loci mapping using genome-wide association mapping.