We developed a eutectic high-entropy alloy (EHEA) with appreciable high-temperature strength-plasticity balance. Structural characterizations of the as-cast sample revealed a lamellar structure with austenite (face-centered-cubic, FCC) and Laves phases. Upon annealing at 873 K, precipitation of nanoscale (Ni, Al, and Zr)-rich L12 phase from the FCC phase took place, which eventually transformed into a martensitic (hexagonal, ε) phase with rearrangement of atomic species. Compressive properties revealed a brittle behavior at temperatures below 873 K, but changed to a ductile behavior with considerable strain hardening at 973 K, due to the formation of a high density of deformation twins observed by transmission electron microscopy.