AAsSe(2) (A = Li, Na) have been identified as a new class of polar direct-band gap semiconductors. These I-V-VI2 ternary alkali-metal chalcoarsenates have infinite single chains of (1/infinity)[AsQ(2)(-)] derived from corner-sharing pyramidal AsQ(3) units with stereochemically active lone pairs of electrons on arsenic. The conformations and packing of the chains depend on the structure-directing alkali metals. This results in at least four different structural types for the Li1-xNaxAsSe2 stoichoimetry (alpha-LiAsSe2, beta-LiAsSe2, gamma-NaAsSe2, and delta-NaAsSe2). Single-crystal X-ray diffraction studies showed an average cubic NaCl-type structure for alpha-LiAsSe2, which was further demonstrated to be locally distorted by pair distribution function (PDF) analysis. The beta and gamma forms have polar structures built of different (1/infinity)[AsSe2-] chain conformations, whereas the delta form has nonpolar packing. A wide range of direct band gaps are observed, depending on composition: namely, 1.11 eV for alpha-LiAsSe2, 1.60 eV for LiAsS2, 1.75 eV for gamma-NaAsSe2, 2.23 eV for NaAsS2. The AAsQ(2) materials are soluble in common solvents such as methanol, which makes them promising candidates for solution processing. Band structure calculations performed with the highly precise screened-exchange sX-LDA FLAPW method confirm the direct-gap nature and agree well with experiment. The polar gamma-NaAsSe2 shows very large nonlinear optical (NLO) second harmonic generation (SHG) response in the wavelength range of 600-950 nm. The theoretical studies confirm the experimental results and show that gamma-NaAsSe2 has the highest static SHG coefficient known to date, 337.9 pm/V, among materials with band gaps larger than 1.0 eV.