This study reports the structure and mechanical properties of a new refractory Ti40Nb30Hf15Al15 (at.%) high entropy alloy. The alloy was fabricated by vacuum arc melting and had a density of 7.07 ± 0.03 g/cm3. After annealing at 1200 °C for 24 h, the alloy possessed a single-phase B2 structure. Further annealing at 600 °C for 24 h resulted in the formation of Widmanstatten (Ti, Al)-rich orthorhombic particles (O-phase) in a bcc matrix. The single-phase B2 alloy demonstrated high (>50%) compressive ductility and a pronounced work hardening capacity. The precipitation of the O-phase particles led to a 50% strength increment at 22 and 600 °C, with some sacrificing in the compressive ductility at 22 °C. The obtained results suggest new approaches to the development of precipitation-strengthened refractory high entropy alloys with a balanced combination of the room- and high-temperature properties.