Top-down engineering of biomolecular circuits to perform specific computational tasks is notoriously hard and time-consuming. Current circuits have limited complexity and are brittle and application-specific. Here we propose an alternative: we design and test a bottom-up constructed Reservoir Computer (RC) that uses random chemical circuits inspired by DNA strand displacement reactions. This RC has the potential to be implemented easily and trained for various tasks. We describe and simulate it by means of a Chemical Reaction Network (CRN) and evaluate its performance on three computational tasks: the Hamming distance and a short- as well as a long-term memory. Compared with the deoxyribozyme oscillator RC model simulated by Yahiro et al., our random chemical RC performs 75.5% better for the short-term and 67.2% better for the long-term memory task. Our model requires an 88.5% larger variety of chemical species, but it relies on random chemical circuits, which can be more easily realized and scaled up. Thus, our novel random chemical RC has the potential to simplify the way we build adaptive biomolecular circuits.