The production of Resistive Plate Chambers (RPCs) for the first Endcap station (RE1) of CMS experiment at Large Hadron Collider (LHC) has started at CERN since June 2004. For good performance of CMS muon and trigger systems these chambers have been assembled in accordance with strict QC (quality control) and QA (quality assurance) procedures during various assembly steps. Up to October 2005, more than 140 chambers have been constructed and more than 100 of them have been tested with cosmic rays. The chambers are assembled with the sensitive volumes (namely gas gaps) which were manufactured in Korea and all relevant mechanical parts were made in China. The procedure of chamber construction and the experience we have accumulated during the assembly will be described.