Density Functional Theory (DFT) and the Hyper-Rayleigh scattering formalism are applied to investigate the frequency-dependent nonlinear optical (NLO) behavior of a novel organometallic chromophore composed of two chalcones bonded by a silver atom. In this investigation, the appropriate LanL2DZ and 6-311++G(d,p) basis sets are applied to describe the metal and the remaining elements, respectively. DFT-based methods which include an accurate description of the exchange Hartree–Fock term are essential to the description of the electrical α, β, and γ properties, which are the optical coefficients discussed. The results indicate that low polarity solvents like benzene improves β and γ values. For instance, from benzene to the water environment, the M06-2X DFT method indicates a decrease from 81.94×103 to 7.12×103 a.u. Moreover, the results in benzene are quite superior to that obtained for urea (0.04×103 a.u.) or 4-nitroaniline (0.73×103 a.u.), which are more standard for NLO materials. The prediction for the second hyperpolarizability (35.37×106 a.u.) is ca. 4.5 times greater than that reported for a single chalcone. The material is suitable for NLO applications.