This work reports on a new method to fabricate mechanically controllable break junctions (MCBJ) with finely adjustable nanogaps between two gold electrodes on solid state chips for characterizing electron transport properties of single molecules. The simple, low cost, robust and reproducible fabrication method combines conventional photolithography, chemical etching and electrodeposition to produce suspended electrodes separated with nanogaps. The MCBJ devices fabricated by the method can undergo many cycles in which the nanogap width can be precisely and repeatedly varied from zero to several nanometers. The method improves the success rate of the MCBJ experiments. Using these devices the electron transport properties of a typical molecular system, commercially available benzene-1,4-dithiol (BDT), have been studied. The I-V and G-V characteristic curves of BDT and the conductance value for a single BDT molecule established the excellent device suitability for molecular electronics research. ; NSF [20620130427]; MOST in China [2007DFC40440, 2009CB930703]; State Key Laboratory of Supramolecular Structure and Materials [SKLSSM200701]; Jilin Univ., China ; CNRS (UMR 8640 'PASTEUR'), Ecole Normale Superieure (ENS), University Pierre and Marie Curie (UPMC) ; French Ministry of Research in France through ANR REEL ; US-NSF [DMR-03-05242]