Additive manufacturing produces net-shaped components layer by layer for engineering applications1-7. The additive manufacture of metal alloys by laser powder bed fusion (L-PBF) involves large temperature gradients and rapid cooling2,6, which enables microstructural refinement at the nanoscale to achieve high strength. However, high-strength nanostructured alloys produced by laser additive manufacturing often have limited ductility3. Here we use L-PBF to print dual-phase nanolamellar high-entropy alloys (HEAs) of AlCoCrFeNi2.1 that exhibit a combination of a high yield strength of about 1.3gigapascals and a large uniform elongation of about 14percent, which surpasses those of other state-of-the-art additively manufactured metal alloys. The high yield strength stems from the strong strengthening effects of the dual-phase structures that consist of alternating face-centred cubic and body-centred cubic nanolamellae; the body-centred cubic nanolamellae exhibit higher strengths and higher hardening rates than the face-centred cubic nanolamellae. The large tensile ductility arises owing to the high work-hardening capability of the as-printed hierarchical microstructures in the form of dual-phase nanolamellae embedded in microscale eutectic colonies, which have nearly random orientations to promote isotropic mechanical properties. The mechanistic insights into the deformation behaviour of additively manufactured HEAs have broad implications for the development of hierarchical, dual- and multi-phase, nanostructured alloys with exceptional mechanical properties.