The new compound LiGaGe2Se6 has been synthesized. It crystallizes in the orthorhombic space group Fdd2 with a = 12.501(3) angstrom, b = 23.683(5) angstrom, c = 7.1196(14) angstrom, and Z = 8. The structure is a three-dimensional framework composed of corner-sharing LiSe4, GaSe4, and GeSe4 tetrahedra. The compound exhibits a powder second harmonic generation signal at 2 mu m that is about half that of the benchmark material AgGaSe2 and possesses a wide band gap of about 2.64(2) eV. LiGaGe2Se6 melts congruently at a rather low temperature of 710 degrees C, which indicates that bulk crystals can be obtained by the Bridgman-Stockbarger technique. According to a first-principles calculation, there is strong hybridization of the 4s and 4p orbitals of Ga, Ge, and Se around the Fermi level. The calculated birefractive index is Delta n = 0.04 for lambda >= 1 mu m, and the calculated major SHG tensor elements are d(15) = 18.6 pm/V and d(33) = 12.8 pm/V. This new material is promising for application in IR nonlinear optics.