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(1) Background: The authenticity of eggs in relation to the housing system of laying hens is susceptible to food fraud due to the potential for egg mislabeling. (2) Methods: A total of 4188 egg yolks, obtained from four different breeds of laying hens housed in colony cage, barn, free-range, and organic systems, were analyzed using 1H NMR spectroscopy. The data of the resulting 1H NMR spectra were used for different machine learning methods to build classification models for the four housing systems. (3) Results: The comparison of the seven computed models showed that the support vector machine (SVM) model gave the best results with a cross-validation accuracy of 98.5%. The test of classification models with eggs from supermarkets showed that only a maximum of 62.8% of samples were classified according to the housing system labeled on the eggs. (4) Conclusion: The classification models developed in this study included the largest sample size compared to the literature. The SVM model is most suitable for evaluating 1H NMR data in terms of the hen housing system. The test with supermarket samples showed that more authentic samples to analyze influencing factors such as breed, feeding, and housing changes are required. [ABSTRACT FROM AUTHOR]