We use electromagnetically-induced-transparency laser cooling to cool motional modes of a linear ion chain. As a demonstration, we apply electromagnetically-induced-transparency cooling on 24Mg+ ions to cool the axial modes of a 9Be+-24Mg+ ion pair and a 9Be+-24Mg+-24Mg+-9Be+ ion chain, thereby sympathetically cooling the 9Be+ ions. Compared to previous implementations of conventional Raman sideband cooling, we achieve approximately an order-of-magnitude reduction in the duration required to cool the modes to near the ground state and significant reduction in required laser intensity.