Physically Unclonable Functions (PUFs) are used to provide identification, authentication and secret key generation based on unique and unpredictable physical characteristics. Carbon Nanotube Field Effect Transistors (CNFETs) were shown to have excellent electrical and unique physical characteristics and are promising candidates to replace silicon transistors in future Very Large Scale Integration (VLSI) designs. We present Carbon Nanotube PUF (CNPUF), the first PUF design that takes advantage of unique CNFET characteristics. CNPUF achieves higher reliability against environmental variations and increased resistance against modeling attacks. Furthermore, CNPUF has a considerable power and energy reduction in comparison to previous ultra-low power PUF designs of 89.6% and 98%, respectively. Additionally, CNPUF allows power-security tradeoff.