Zika virus is a single-stranded, positive-sense RNA virus of the family Flaviviridae, which has recently undergone a rapid expansion among humans in the Western Hemisphere. Here, we report a high-resolution map of ribosomal occupancy of the Zika virus genome during infection of mammalian and insect cells, obtained by ribosome profiling. In contrast to some other flaviviruses such as West Nile, we find no evidence for substantial frameshift-induced ribosomal drop-off during translation of the viral polyprotein, indicating that Zika virus must use alternative mechanisms to downregulate levels of catalytically active viral polymerase. We also show that high levels of ribosome-protected fragments map in-frame to two previously overlooked upstream open reading frames (uORFs) initiating at CUG and UUG codons, with likely consequences for the efficiency of polyprotein expression. Curiously, in African isolates of Zika virus, the two uORFs are fused in-frame into a single uORF. A parallel RNA-Seq analysis reveals the 5' end position of the subgenomic flavivirus RNA in mammalian and insect cells. Together, these provide the first analysis of flavivirus gene expression by ribosome profiling.