Background: Zika virus (ZIKV) and chikungunya virus (CHIKV) are highly pathogenic arthropod-borne viruses that are currently a serious health burden in the Americas, and elsewhere in the world. ZIKV and CHIKV co-circulate in the same geographical regions and are mainly transmitted by Aedes aegypti mosquitoes. There is a growing number of case reports of ZIKV and CHIKV co-infections in humans, but it is uncertain whether co-infection occurs via single or multiple mosquito bites. Here we investigate the potential of Ae. aegypti mosquitoes to transmit both ZIKV and CHIKV in one bite, and we assess the consequences of co-infection on vector competence. Methodology/Principal findings: First, growth curves indicated that co-infection with CHIKV negatively affects ZIKV production in mammalian, but not in mosquito cells. Next, Ae. aegypti mosquitoes were infected with ZIKV, CHIKV, or co-infected via an infectious blood meal or intrathoracic injections. Infection and transmission rates, as well as viral titers of positive mosquitoes, were determined at 14 days after blood meal or 7 days after injection. Saliva and bodies of (co-)infected mosquitoes were scored concurrently for the presence of ZIKV and/or CHIKV using a dual-colour immunofluorescence assay. The results show that orally exposed Ae. aegypti mosquitoes are highly competent, with transmission rates of up to 73% for ZIKV, 21% for CHIKV, and 12% of mosquitoes transmitting both viruses in one bite. However, simultaneous oral exposure to both viruses did not change infection and transmission rates compared to exposure to a single virus. Intrathoracic injections indicate that the selected strain of Ae. aegypti has a strong salivary gland barrier for CHIKV, but a less profound barrier for ZIKV. Conclusions/Significance: This study shows that Ae. aegypti can transmit both ZIKV and CHIKV via a single bite. Furthermore, co-infection of ZIKV and CHIKV does not influence the vector competence of Ae. aegypti.