The translational control of oncoprotein expression is implicated in many cancers. Here we report an eIF4A RNA helicase-dependent mechanism of translational control that contributes to oncogenesis and underlies the anticancer effects of silvestrol and related compounds. For example, eIF4A promotes T-cell acute lymphoblastic leukaemia development in vivo and is required for leukaemia maintenance. Accordingly, inhibition of eIF4A with silvestrol has powerful therapeutic effects against murine and human leukaemic cells in vitro and in vivo. We use transcriptome-scale ribosome footprinting to identify the hallmarks of eIF4A-dependent transcripts. These include 5' untranslated region (UTR) sequences such as the 12-nucleotide guanine quartet (CGG)4 motif that can form RNA G-quadruplex structures. Notably, among the most eIF4A-dependent and silvestrol-sensitive transcripts are a number of oncogenes, superenhancer-associated transcription factors, and epigenetic regulators. Hence, the 5' UTRs of select cancer genes harbour a targetable requirement for the eIF4A RNA helicase.