Zika is an emerging, mosquito-borne virus recently introduced to the Americas, whose rapid spread is unprecedented and of great public health concern. Knowledge about transmission -- which depends on the presence of competent vectors -- remains incomplete, especially concerning potential transmission in geographic areas in which it has not yet been introduced. To identify presently unknown vectors of Zika, we developed a data-driven model linking candidate vector species and the Zika virus via vector-virus trait combinations that confer a propensity toward associations in the larger ecological network connecting flaviviruses and their mosquito vectors. Our model predicts that thirty-five species may be able to transmit the virus, twenty-six of which are not currently known vectors of Zika virus. Seven of these species are found in the continental United States, including Culex quinquefasciatus and Cx. pipiens, both of which are common mosquito pests and vectors of West Nile Virus. Because the range of these predicted species is wider than that of known vectors Aedes aeygpti and Ae. albopictus, we reason that a larger geographic area is at risk for autochthonous transmission of Zika virus than reported by maps constructed from the ranges of only the two Aedes species. Consequently, the reach of existing vector control activities and public health campaigns may need to be expanded.