Chemical vapour deposition (CVD) synthesis of graphene on copper has been broadly adopted since the first demonstration of this process1. However, widespread use of CVD-grown graphene for basic science and applications has been hindered by challenges with reproducibility2 and quality3. Here we identify trace oxygen as a key factor determining the growth trajectory and quality for graphene grown by low-pressure CVD. Oxygen-free chemical vapour deposition (OF-CVD) synthesis is fast and highly reproducible, with kinetics that can be described by a compact model, whereas adding trace oxygen leads to suppressed nucleation and slower/incomplete growth. Oxygen affects graphene quality as assessed by surface contamination, emergence of the Raman D peak and decrease in electrical conductivity. Epitaxial graphene grown in oxygen-free conditions is contamination-free and shows no detectable D peak. After dry transfer and boron nitride encapsulation, it shows room-temperature electrical-transport