We show experimental and numerical results of the competition between two small sinusoidal inputs that try to phase synchronize to a chaotic Chua circuit. Our observations indicate that depending on the values of amplitude and frequency of the two sinusoidal functions, the Chua oscillator can stay phase synchronized to one of the inputs all the time, or can alternate synchronous states between them (*). This is a natural extension of the case where one periodic function entrains a chaotic oscillator. It can be regarded as a next step toward more complicated synchronization processes involving multiple oscillators. (*) R. Breban and E. Ott, Phys. Rev. E 65, 056219 (2002).