Acutely ill adults with hypoxaemic respiratory failure admitted to the intensive care unit (ICU) are at risk of life-threatening hypoxia, and thus oxygen is administered. However, the evidence on the optimal level of oxygenation is of low quantity and quality with no firm evidence for benefit or harm. Importantly, liberal use of supplementary oxygen may increase the number of serious adverse events including death. The aim of the HOT-ICU trial is to assess the benefits and harms of two targets of partial pressure of oxygen in arterial blood (PaO2) in guiding the oxygen administration in acutely ill adults with hypoxaemic respiratory failure at ICU admission.