Understanding and controlling the growth kinetics of graphene is a prerequisite to synthesize this highly wanted material by chemical vapor deposition on Cu, e.g. for the construction of ultra-stable electron transparent membranes. It is reviewed that Cu foils contain a considerable amount of carbon in the bulk which significantly exceeds the expected amount of thermally equilibrated dissolved carbon in Cu and that this carbon must be removed before any high quality graphene may be grown. Starting with such conditioned Cu foils, systematic studies of the graphene growth kinetics in a reactive CH 4 /H 2 atmosphere allow to extract the following meaningful data: prediction of the equilibrium constant of the graphene formation reaction within a precision of a factor of two, the confirmation that the graphene growth proceeds from a C(ad)-phase on Cu which is in thermal equilibrium with the reactive gas phase, its apparent activation barrier and finally the prediction of the achievable growth velocity of the growing graphene flakes during chemical vapor deposition. As a result of the performed study, growth parameters are identified for the synthesis of high quality monolayer graphene with single crystalline domains of 100-1000 μm in diameter within a reasonable growth time.