The Yale-Weizmann collaboration aims to develop a low-radioactivity (low-background) cryogenic noble liquid detector for Dark-Matter (DM) search in measurements to be performed deep underground as for example carried out by the XENON collaboration. A major issue is the background induced by natural radioactivity of present-detector components including the Photo Multiplier Tubes (PMT) made from glass with large U-Th content. We propose to use advanced Thick Gaseous Electron Multipliers (THGEM) recently developed at the Weizmann Institute of Science (WIS). These hole-multipliers will measure in a two-phase (liquid/gas) Xe detector electrons extracted into the gas phase from both ionization in the liquid as well as scintillation-induced photoelectrons from a CsI photocathode immersed in LXe. We report on initial tests (in gas) of THGEM made out of Cirlex (Kapton) which is well known to have low Ra-Th content instead of the usual G10 material with high Ra-Th content.