In this work we develop a model of predictive learning on neuromorphic hardware. Our model uses the on-chip plasticity capabilities of the Loihi chip to remember observed sequences of events and use this memory to generate predictions of future events in real time. Given the locality constraints of on-chip plasticity rules, generating predictions without interfering with the ongoing learning process is nontrivial. We address this challenge with a memory consolidation approach inspired by hippocampal replay. Sequence memory is stored in an initial memory module using spike-timing dependent plasticity. Later, during an offline period, memories are consolidated into a distinct prediction module. This second module is then able to represent predicted future events without interfering with the activity, and plasticity, in the first module, enabling online comparison between predictions and ground-truth observations. Our model serves as a proof-of-concept that online predictive learning models can be deployed on neuromorphic hardware with on-chip plasticity.