Radio frequency identification (RFID) is a promising wireless sensor technology in the Internet of Things and can be applied for object identification. However, the security issues are still open challenges and should be addressed to achieve enhanced safeguard. Existing security solutions mainly apply logical operators, hash function, and other cryptographic primitives to design authentication schemes. In this paper, we propose a Chebyshev chaotic map-based authentication protocol (C2MP) for the RFID applications. Thereinto, Chebyshev polynomial's semigroup and chaotic properties are introduced for identity authentication and anonymous data transmission. The proposed C2MP owns the security properties including data integrity, authentication, anonymity, and session freshness. According to the BAN logic, security formal analysis is performed based on the messages formalization, initial assumptions, anticipant goals, and logic verification. It indicates that the proposed C2MP is suitable for universal RFID applications.