Physical unclonable function (PUF) is an advanced hardware security technology. Most conventional encryption approaches rely on the secure keys stored in nonvolatile memory, which are vulnerable to physical attacks. In contrast, PUF exploits the hardware fabrication variations to generate secure keys. As there are significant fabrication induced variations in carbon nanotube (CNT)-based circuits, they are natural candidates for building highly secure PUFs. However, existing PUFs are reported to be vulnerable to machine learning modeling attacks. In this paper, we develop a novel CNT PUF design through leveraging Lorenz chaotic system. Lorenz chaotic system magnifies the differences among responses of similar challenges. This salient feature gives the superior security performance, making the PUF design resistant to machine learning modeling attacks. Our experimental results demonstrate that these attacking methods can achieve very high bit-wise prediction rates for the standard CNT PUF. In contrast, when hacking the proposed Lorenz chaotic system-based CNT PUF, they become much less effective, where only up to 55% bit-wise prediction rates can be achieved.