A novel high-efficiency and noise-robust differential chaos shift keying (DCSK) communication approach based on an analytically solvable chaotic oscillator (ASCO) is proposed. Due to the special characteristic of the ASCO that provides predictability over specific intervals of every binary symbol period, the proposed communication system requires no reference signal like conventional DCSK systems, which can double the data transmission rate. Meanwhile, the originally transmitted binary information can be recovered by conducting integration processing of the received signal over the specific intervals of every binary symbol period, even under strong noise conditions, which provides a low bit error rate (BER). Simulations are conducted to verify that the proposed DCSK approach provides a much lower BER than conventional DCSK approaches.