The compound CaV₂O₄ contains V+3 cations with spin S=1 and has an orthorhombic structure at room temperature containing zigzag chains of V atoms running along the c axis. We have grown single crystals of CaV₂O₄ and report crystallography, static magnetization, magnetic susceptibility χ, ac magnetic susceptibility, heat capacity C_p, and thermal expansion measurements in the temperature T range of 1.8–350 K on the single crystals and on polycrystalline samples. An orthorhombic-to-monoclinic structural distortion and a long-range antiferromagnetic (AF) transition were found at sample-dependent temperatures T_S≈108–145 K andT_N≈51–76 K, respectively. In two annealed single crystals, another transition was found at ≈200 K. In one of the crystals, this transition is mostly due to V₂O₃ impurity phase that grows coherently in the crystals during annealing. However, in the other crystal the origin of this transition at 200 K is unknown. The χ(T) shows a broad maximum at ≈300 K associated with short-range AF ordering and the anisotropy of χ above T_N is small. The anisotropic χ(T→0) data below T_N show that the (average) easy axis of the AF magnetic structure is the b axis. The C_p(T) data indicate strong short-range AF ordering above T_N, consistent with the χ(T) data. We fitted our χ data by a J₁-J₂ S=1 Heisenberg chain model, where J₁(J₂) is the (next)-nearest-neighbor exchange interaction. We find J₁≈230 K and surprisingly, J₂/J₁≈0 (or J₁/J₂≈0). The interaction J_⊥ between these S=1 chains leading to long-range AF ordering at T_N is estimated to be J_⊥/J₁≳0.04.