The novel Hf25Sc25Ti25Zr25 (at.%) equiatomic alloy comprised of hexagonal solid solutions was designed and cast by arc melting of high purity elemental precursors. The predominant volume of the as-cast state exhibited a hexagonal structure and near-equal atomic concentrations of elements. Traces of the second hexagonal phase with a content not exceeding 6 vol.% were located in regions between coarse laths of the acicular matrix. The as-cast alloy subjected to room temperature compression developed very strong hardening effect resulting in high strength of 1802 MPa and yield stress of 698 MPa. After deformation, frequent slip bands within the solid solution matrix along with high density of dislocations were present. The new alloy showed high thermal stability. Annealing at 1000 °C for 5 h led to dissolution of Ti enriched solid solution and to precipitation of the Sc plate-like phase with cubic structure embedded in the hexagonal matrix. As a result, only a slight reduction in compressive properties, as compared to the as-cast state, was experienced. An assessment of the quantum mechanical approach to the alloy developed was conducted by calculations of structural and elastic properties based on the atomistic-level model of the alloy in the framework of the density functional theory.