The new compound BaGa(4)Se(7) has been synthesized for the first time. It crystallizes in the monoclinic space group Pc with a = 7.6252 (15) Å, b = 6.5114 (13) Å, c = 14.702 (4) Å, β = 121.24 (2)°, and Z = 2. In the structure, GaSe(4) tetrahedra share corners to form a three-dimensional framework with cavities occupied by Ba(2+) cations. The material is a wide-band gap semiconductor with the visible and IR optical absorption edges being 0.47 and 18.0 μm, respectively. BaGa(4)Se(7) melts congruently at 968 °C and exhibits a second harmonic generation response at 1 μm that is approximately 2-3 times that of the benchmark material AgGaS(2). A first-principles calculation of the electronic structure, linear and nonlinear optical properties of BaGa(4)Se(7) was performed. The calculated birefractive indexΔn = 0.08 at 1 μm and the major SHG tensor elements are: d(11) = 18.2 pm/V and d(13) = -20.6 pm/V. This new material is a very promising NLO crystal for practical application in the IR region.