The present work deals with the fabrication of Ti-6Al-4V in situ alloyed with 3.5 wt.% Cu (Ti-6Al-4V-3.5Cu), its microstructural evolution, and its related tensile properties. Specimens with a relative density of 99 +/- 0.1% presented a microstructure that differed from that of pure Ti-6Al-4V in LPBF, which usually exhibits a fully martensitic structure (alpha '). In Ti-6Al-4V-3.5Cu, apart from alpha-Ti, beta-Ti, and intermetallic Ti2Cu were also observed, generated by in situ martensite decomposition. Initially solidified large columnar beta-Ti grains underwent a martensitic transformation to alpha '. Cyclic reheating caused by layer-wise deposition during LPBF enabled the diffusion of Cu and V, allowing the transformation of alpha ' to stable alpha-Ti and the precipitation of beta-Ti and Ti2Cu. The alpha ' decomposition and formation of beta-Ti and Ti2Cu contributed to an UTS of 1362 +/- 14 MPa and an Rp0.2 of 1313 +/- 14 MPa in the horizontal specimen orientation in the as-built state. The elongation at fracture was 3.9 +/- 0.6%. In the vertical orientation, the specimens exhibited an UTS of 1305 +/- 19 MPa, an Rp0.2 of 1215 +/- 23 MPa, and an elongation at fracture of 5.4 +/- 1.5%. Stress-relief annealing reduced the UTS and Rp0.2 to 1099 +/- 6 MPa and 1014 +/- 5 MPa, respectively, with an increase in elongation at fracture to 6.7 +/- 0.4% in the horizontal specimen orientation. In the vertical specimen orientation, stress relief annealing resulted in an UTS of 1051 +/- 13 MPa and an Rp0.2 of 926 +/- 18 MPa. The elongation at fracture was increased to 11.3 +/- 1.3%.