Chikungunya fever (CHIKV), a viral disease transmitted by mosquitoes, is currently affecting several territories in the Caribbean. The vector is found in the Americas from South Florida to Brazil and the Caribbean is a highly connected region. There is therefore a significant risk for the epidemic to quickly expand to a wide area in the Americas, and of introduction to Europe where competent vectors are present. Here, we describe the spread of CHIKV in the first three territories to report cases and between territories of the region. Local transmission of CHIKV in the Caribbean is found to be very effective (mean number of cases generated by a human case in the range 2 to 4). There is a strong spatial signature in the regional epidemic, with the risk of transmission between territories estimated to be inversely proportional to the distance rather than being driven by air transportation. So far, this simple model has successfully predicted observed patterns of spread. The spatial structure allows ranking territories according to their current risk of invasion. This characterization may help national and international agencies to optimize resource allocation for monitoring and control and encourage territories with elevated risks to act. This is important to reduce the risk of dissemination to other parts of the world, including Europe.