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Chaotic synchronization is investigated experimentally using two diode lasers as transmitter and receiver. The transmitter laser is rendered chaotic by application of an optical feedback in an external-cavity configuration. Experimental conditions are found under which the synchronization diagram makes a transition from a positive to a negative gradient. A regime of operating conditions is identified in which the receiver laser is found to anticipate the dynamics of the transmitter laser. The anticipation time does not depend on the external-cavity length, but rather on the time of flight between the two lasers. Changes in the spectrum of the synchronized system are shown to be associated with the transition between anticipating and lag synchronization.