Rearrangements that change the connectivity of a carbon skeleton are often useful in synthesis, but it can be difficult to follow their mechanisms. Scanning probe microscopy can be used to manipulate a skeletal rearrangement at the single-molecule level, while monitoring the geometry of reactants, intermediates and final products with atomic resolution. We studied the reductive rearrangement of 1,1-dibromo alkenes to polyynes on a NaCl surface at 5 K, a reaction that resembles the Fritsch-Buttenberg-Wiechell rearrangement. Voltage pulses were used to cleave one C-Br bond, forming a radical, then to cleave the remaining C•-Br bond, triggering the rearrangement. These experiments provide structural insight into the bromo-vinyl radical intermediates, showing that the C=C•-Br unit is nonlinear. Long polyynes, up to the octayne Ph-(C≡C)8-Ph, have been prepared in this way. The control of skeletal rearrangements opens a new window on carbon-rich materials and extends the toolbox for molecular synthesis by atom manipulation.