In this work, we investigate differential chaos shift keying (DCSK), a communication-based waveform, in the context of wireless power transfer (WPT). Particularly, we present a DCSK-based WPT architecture, that employs an analog correlator at the receiver in order to boost the energy harvesting (EH) performance. By taking into account the nonlinearities of the EH process, we derive closed-form analytical expressions for the peak-to-average-power-ratio of the received signal as well as the harvested power. Nontrivial design insights are provided, where it is shown how the parameters of the transmitted waveform affects the EH performance. Furthermore, it is demonstrated that the employment of a correlator at the receiver achieves significant EH gains in DCSK-based WPT systems.