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Observationally, the mysterious fast radio bursts (FRBs) are classified as repeating ones and apparently non-repeating ones. While repeating FRBs cannot be classified into the non-repeating group, it is unknown whether the apparently non-repeating FRBs are actually repeating FRBs whose repetitions are yet to be discovered, or whether they belong to another physically distinct type from the repeating ones. In a series of two papers, we attempt to disentangle this mystery with machine learning methods. In this first paper, we focus on an array of supervised machine learning methods. We train the machine learning algorithms with a fraction of the observed FRBs in the first CHIME/FRB catalog, telling them which ones are apparently non-repeating and which ones are repeating. We then let the trained models predict the repetitiveness of the rest of the FRB data with the observed parameters, and we compare the predictions with the observed repetitiveness. We find that the models can predict most FRBs correctly, hinting towards distinct mechanisms behind repeating and non-repeating FRBs. We also find that the two most important distinguishing factors between non-repeating and repeating FRBs are brightness temperature and rest-frame frequency bandwidth. By applying the trained models back to the entire first CHIME catalog, we further identify some potentially repeating FRBs currently reported as non-repeating. We recommend a list of these bursts as targets for future observing campaigns to search for repeated bursts in a combination with the results presented in Paper II using unsupervised machine learning methods.