Use of a high-pressure coolant supply (HPC) can lead to a considerable improvement in machining performance and process stability during the cutting of difficult materials such as stainless steels. Due to the high pressure of the coolant jet, a hydraulic wedge was formed at the tool–chip interface and thus reduced tool–chip contact length and friction behavior. Moreover, the cutting stability can be enhanced as a result of efficient chip breakability. The goal of this work is to evaluate how chip morphology is influenced by three thin jets of pressurized coolant directed into the tool–chip interface during machining of AISI 304 austenitic stainless steel and compare the resulting performance of the tool with dry and conventional coolant conditions. Furthermore, this research evaluates the influence of tool wear on the chip forming mechanism during the turning process. An analysis of the chip generated under machining emphasizes the hypothesis that variations in the cutting tool wear directly affect the chip shape and type of chip segmentation. Finally, a theoretical model was developed to predict the chip upcurl radius under HPC machining. This model is based on shear plane and structural mechanical theories which evaluate plastic strain and the bending moments along the length of the curled chip. The chip upcurl radius values from the developed theoretical model were found to be in good agreement with those measured in the machining tests.