An experimental system based on a transmission electron microscope JEM-100CX has been developed for electron beam-induced chemical vapor deposition. Direct electron beam-induced growth of nanometer-wide self-supporting rods has been performed inside the microscope operating in scanning mode by decomposition of carbonyls of chromium Cr(CO)₆, tungsten W(CO)₆, and rhenium Re₂(CO)₁₀. In situ phase and structure transformations under annealing inside the microscope column were studied. Nanoscale rods and strips grown from rhenium carbonyl are of special interest because, after annealing, they consist of a single pure rhenium phase. The described method of metallic nanoelements fabrication enables us to produce highly conductive nanowires and tips for application in nanoelectronics, emission electronics, and scanning tunneling microscopy.