A reactor (9) for the pyrolysis of carbon-containing waste material such as rubber chips includes a cylindrical air-tight reactor vessel (10) which has an inlet through which rubber chips (4) are introduced into the reactor vessel and an outlet (60) through which oil distillate can be discharged therefrom. The reactor vessel has a cooling jacket through which cooling water flows for cooling an inner shell (40) of the vessel. The chips (4) are deposited onto a support tray (70) and displaced towards a rear end of the reactor vessel by a chain conveyer (89). The chips (4) are heated on the tray (40) causing decomposition of the chips into a vapor and amorphous carbon. The vapor condenses when it contacts the inner shell (40) and runs down the sides of the vessel (10) towards a lower side thereof before being discharged through the outlet (60).