A physical unclonable function (PUF) is a promising lightweight circuit that provides security and authentication capability for electronic devices with low computational resources. Among various PUFs, the bistable ring PUF (BR-PUF) is considered one of the robust configurations. However, it has been shown that the challenge-response pairs (CRPs) from BR-PUF are vulnerable to statistical machine learning (ML) attacks, such as k-junta learning, support vector machine (SVM), and logistic regression (LR). In this article, we first show that the k-junta attack can break CRPs from the BR-PUF. Then, we present a hybrid chaotic-BR-PUF structure that obfuscates the BR-PUF response with the nonlinearized chaotic response. The proposed PUF structure has been implemented and experimentally evaluated on Xilinx Artix-7 FPGA, and the PUF measurements were captured. The proposed PUF was tested with a powerful statistical method developed using k-junta-based learning to confirm its strength against such attacks and evaluated using CRPs collected. The proposed PUF provides better resistance against ML attacks and reduces the learning accuracy to 50%–60% compared with previously proposed PUFs.