The invention relates to a unit (14) for holding a tool (10) for chuck (7) mounting heads (6) used in machining where chips are removed from the worked part and waste material consequently produced. The unit comprises: a tool (10) holder spindle (15) designed to be attached to the chuck (7) of the head (6); and an extraction device (18) associated to the spindle (15) and comprising an annular manifold (69) comprising a first pipe (19) which extends from a first end (20) giving onto an area (B) close to the tool (10) and ends at a second end (21) equipped with a first union (73) designed to be quickly connected with the inside of a second union (74) which matches the first and which is located at a connection unit (39) associated to the chuck (7) mounting head (6); said first and second unions (73, 74) forming a detachable coupling (42) designed to connect the extraction device (18), through a second pipe (43), to a pump (46) that creates a flow of fluid at a defined pressure along the first pipe (19) so as to remove the waste material produced by machining from the area (B) close to the tool (10).