A new cylindrical drift chamber is currently under construction for the MEG II experiment. The chamber is meant to track low momentum positrons from μ+ decays to search for μ+→e+γ events. The detector is segmented in very small drift cells, placed in stereo configuration and operated in a helium–isobutane gas mixture. The use of thin aluminium wires and light gas mixture set the total radiation length of the chamber to only 1.6×10−3X0 per track turn allowing for a momentum resolution of ~120keV/c.