A novel detector for ionization signals in a single phase LAr-TPC has been experimented in the ICARINO test facility at the INFN Laboratories in Legnaro. It is based on the adoption of a multilayer Large Electron Multiplier (LEM) replacing the traditional anodic wire arrays. Cosmic muon tracks were detected allowing the measurement of energy deposition and a first determination of the signal to noise ratio. The analysis of the recorded events demonstrated the 3D reconstruction capability of this device for ionizing events in liquid Argon. The collected fraction of ionization charge is close to about 90%, with signal to noise ratio similar to that measured with more traditional wire chambers.