Securing radio frequency identification (RFID) systems against malicious attacks such as eavesdropping is a highly challenging task due to the resource constrained nature of such systems. In fact, the modest computational and storage capabilities of RFID tags makes it impossible to adopt classical cryptographic techniques. While existing work has mostly focused on lightweight cryptographic techniques, in this paper, the first analysis on the adoption of physical layer security techniques in an RFID system is presented. First, the secrecy rate of ultra high frequency (UHF) RFID backscatter systems is characterized. Then, a novel approach is proposed for maximizing this secrecy rate by exploiting the nature and features of the RFID backscatter channel. To explore these features, the proposed approach allows the RFID readers to append artificial noise signals to their continuous wave (CW) signals which then propagate via the backscatter channel hence inducing interference at the eavesdroppers. For enabling the readers to optimally allocate power between their CW signals and artificial noise, a noncooperative game is formulated using which the readers can decide on their optimal power allocations so as to maximize their overall secrecy rates, given the ensuing inter-reader interference. For solving this game, a best response algorithm is proposed using which the readers can reach a Nash equilibrium. Simulation results show that the proposed approach yields significant performance gains, in terms of the average secrecy rate per RFID reader, of at least 17% relative to the classical RFID operation.