We demonstrate experimentally the efficiency of a recently proposed scheme of terahertz generation based on Cherenkov emission from ultrashort laser pulses in a sandwich structure. The structure has a thin nonlinear core covered with a prism of low terahertz absorption. Using an 8 mm long Si-LiNbO(3)-BK7 structure with a 50 microm thick LiNbO(3) core, we converted 40 microJ, 50 fs Ti:sapphire laser pulses into terahertz pulses of approximately 3 THz bandwidth with a record efficiency of over 0.1%.