An essential issue in developing semiconductor devices for photovoltaics and thermoelectrics is to design materials with appropriate band gaps plus the proper positioning of dopant levels relative to the bands. Local density (LDA) and generalized gradient approximation (GGA) density functionals generally underestimate band gaps for semiconductors and sometimes incorrectly predict a metal. Hybrid functionals that include some exact Hartree-Fock exchange are known to be better. We show here for CuInSe_2, the parent compound of the promising CIGS Cu(In_xGa_(1-x))Se_2 solar devices, that LDA and GGA obtain gaps of 0.0-0.01 eV (experiment is 1.04 eV), while the historically first global hybrid functional, B3PW91, is surprisingly better than B3LYP with band gaps of 1.07 and 0.95 eV, respectively. Furthermore, we show that for 27 related binary and ternary semiconductors, B3PW91 predicts gaps with a mean average deviation (MAD) of only 0.09 eV, which is substantially better than all modern hybrid functionals.