This paper introduces a novel technique that enables access by a cognitive secondary user (SU) to a spectrum occupied by an incumbent primary user (PU) that employs Type-I Hybrid ARQ. The technique allows the SU to perform selective retransmissions of SU data packets that have not been successfully decoded in the previous attempts. The temporal redundancy introduced by the PU ARQ protocol and by the selective retransmission process of the SU can be exploited by the SU receiver to perform interference cancellation (IC) over multiple transmission slots, thus creating a "clean" channel for the decoding of the concurrent SU or PU packets. The chain decoding technique is initiated by a successful decoding operation of a SU or PU packet and proceeds by an iterative application of IC in order to decode the buffered signals that represent packets that could not be decoded before. Based on this scheme, an optimal policy is designed that maximizes the SU throughput under a constraint on the average long-term PU performance. The optimality of the chain decoding protocol is proved, which determines which packet the SU should send at a given time. Moreover, a decoupling principle is proved, which establishes the optimality of decoupling the secondary access strategy from the chain decoding protocol. Specifically, first, the SU access policy, optimized via dynamic programming, specifies whether the SU should access the channel or not, based on a compact state representation of the protocol; and second, the chain decoding protocol embeds four basic rules that are used to determine which packet should be transmitted by the SU. Chain decoding provably yields the maximum improvement that can be achieved by any scheme under our assumptions, and thus it is the ultimate scheme, which completely closes the gap between previous schemes and optimality.