An adaptor for setting a self-drilling, chemically anchorable, fastening element (5) includes a rotor member (21) rotatably supported in the adaptor housing (36) and having at its opposite ends (23,25) respectively, a coupling section (24) for connecting the rotor member (21) with a drilling tool (8) for joint rotation therewith, and a coupling receptacle (26) for fixedly receiving a free end (6) of the fastening element (5). Support elements (52,53) are provided in one of two housing parts (41,51) for rotatably supporting the rotor member (21). Sealing elements (42), which are provided in another housing part (41), for a connection channel section (32) that connects a connection opening (37) in the housing (36) for the ejection medium (4) with a feeding channel (31) in the rotor member (21).