A portable countersinking device, comprising: an internal bore positioner adapted to be received by a bore defined by a workpiece, wherein the internal bore positioner comprises a collet configured to be actuatable between a contracted arrangement, for allowing the collet to be inserted into and removed from the bore, and an expanded arrangement, for securing the collet at a selected depth within the bore; a driver rod engaged with the internal bore positioner and extending outwardly of the bore through a bore opening in a surface of the workpiece; a centering chuck engaged about the driver rod, the centering chuck being axially movable along the driver rod and being configured to engage the bore opening so as to cooperate with the internal bore positioner to align the driver rod along a longitudinal axis of the bore; a counterbore engaged about the driver rod, opposite the centering chuck from the internal bore positioner, the counterbore being rotatable about the driver rod and configured to be axially advanced along the driver rod to engage the bore opening and to countersink the bore; and a countersink depth control arrangement associated with the counterbore and configured to cooperate therewith to countersink the bore to a predetermined depth, a mandrel coaxially engaged with the driver rod, the mandrel being axially movable between a contracted position and an extended position with respect to the driver rod by a pneumatic actuator engaged therewith, the mandrel being received by the collet such that, in the extended position of the mandrel, the collet is in the contracted arrangement and, in the contracted position of the mandrel, the collet is in the expanded arrangement, a shroud extending about the driver rod and the counterbore, wherein the shroud is configured to be advanced toward the collet in response to axial movement of the mandrel to the contracted position to actuate the collet to the expanded position. an internal bore positioner adapted to be received by a bore defined by a workpiece, wherein the internal bore positioner comprises a collet configured to be actuatable between a contracted arrangement, for allowing the collet to be inserted into and removed from the bore, and an expanded arrangement, for securing the collet at a selected depth within the bore; a driver rod engaged with the internal bore positioner and extending outwardly of the bore through a bore opening in a surface of the workpiece; a centering chuck engaged about the driver rod, the centering chuck being axially movable along the driver rod and being configured to engage the bore opening so as to cooperate with the internal bore positioner to align the driver rod along a longitudinal axis of the bore; a counterbore engaged about the driver rod, opposite the centering chuck from the internal bore positioner, the counterbore being rotatable about the driver rod and configured to be axially advanced along the driver rod to engage the bore opening and to countersink the bore; and a countersink depth control arrangement associated with the counterbore and configured to cooperate therewith to countersink the bore to a predetermined depth, a mandrel coaxially engaged with the driver rod, the mandrel being axially movable between a contracted position and an extended position with respect to the driver rod by a pneumatic actuator engaged therewith, the mandrel being received by the collet such that, in the extended position of the mandrel, the collet is in the contracted arrangement and, in the contracted position of the mandrel, the collet is in the expanded arrangement, a shroud extending about the driver rod and the counterbore, wherein the shroud is configured to be advanced toward the collet in response to axial movement of the mandrel to the contracted position to actuate the collet to the expanded position.