Proteins are particularly prone to aggregation immediately after release from the ribosome, and it is therefore important to elucidate the role of chaperones during these key steps of protein life. The Hsp70 and trigger factor (TF) chaperone systems interact with nascent proteins during biogenesis and immediately post-translationally. It is unclear, however, whether these chaperones can prevent formation of soluble and insoluble aggregates. Here, we address this question by monitoring the solubility and structural accuracy of globin proteins biosynthesized in an Escherichia coli cell-free system containing different concentrations of the bacterial Hsp70 and TF chaperones. We find that Hsp70 concentrations required to grant solubility to newly synthesized proteins are extremely sensitive to client-protein sequence. Importantly, Hsp70 concentrations yielding soluble client proteins are insufficient to prevent formation of soluble aggregates. In fact, for some aggregation-prone protein variants, avoidance of soluble-aggregate formation demands Hsp70 concentrations that exceed cellular levels in E. coli. In all, our data highlight the prominent role of soluble aggregates upon nascent-protein release from the ribosome and show the limitations of the Hsp70 chaperone system in the case of highly aggregation-prone proteins. These results demonstrate the need to devise better strategies to prevent soluble-aggregate formation upon release from the ribosome.