When aiming to assess the fat composition of commercial potato chip products, their diversity and the difficulties to verify the nutritional label of batches of chips by official methods are main challenges. Thus, the possibility of using alternative technologies is of great interest for both the industry and the public administration. Near-infrared spectroscopy (NIRS) is a rapid and non-destructive technique that has been proven useful in different applications in the food industry. However, suitable specific treatments of compositional references with NIRS methods have been until now very scarce in the literature. The nutritional label information is commonly given as percentage content values across several nutritional categories. This formally corresponds with the class of so-called compositional data, for which there are specific statistical methods. This study contributes to ongoing research on the feasibility of Vis/NIR spectroscopy for food nutritional labelling. In particular, a calibration model is formulated to estimate the relative content of fat in potato chips products based on NIR spectral signal that integrates a consistent statistical treatment of the nutritional reference data. The method provides accurate estimates of the fat composition, with this including saturated, monounsaturated, and polyunsaturated types of fat, as well as their total fat percentage (cross-validated overall R2 = 0.88 and R2 = 0.82 from ground and fragmented samples respectively) and shows its potential for both nutritional labelling and verification in a rapid and inexpensive manner.