Organs-on-chips are microfluidic systems with controlled, dynamic microenvironments in which cultured cells exhibit functions that emulate organ-level physiology. They can in principle be 'personalised' to reflect individual physiology, for example by including blood samples, primary human tissue, and cells derived from induced pluripotent stem cell-derived cells, as well as by tuning key physico-chemical parameters of the cell culture microenvironment based on personal health data. The personalised nature of such systems, combined with physiologically relevant read-outs, provides new opportunities for person-specific assessment of drug efficacy and safety, as well as personalised strategies for disease prevention and treatment; together, this is known as 'precision medicine'. There are multiple reports of how to personalise organs-on-chips, with examples including airway-on-a-chip systems containing primary patient alveolar epithelial cells, vessels-on-chips with shapes based on personal biomedical imaging data and lung-on-a-chip systems that can be exposed to various regimes of cigarette smoking. In addition, multi-organ chip systems even allow the systematic and dynamic integration of more complex combinations of personalised cell culture parameters. Current personalised organs-on-chips have not yet been used for precision medicine as such. The major challenges that affect the implementation of personalised organs-on-chips in precision medicine are related to obtaining access to personal samples and corresponding health data, as well as to obtaining data on patient outcomes that can confirm the predictive value of personalised organs-on-chips. We argue here that involving all biomedical stakeholders from clinicians and patients to pharmaceutical companies will be integral to transition personalised organs-on-chips to precision medicine.