A chest press exercise machine has a self-aligning pivoting user support on a main frame and an exercise arm which is linked to the pivoting user support to translate movement of the exercise arm into movement of the user support. A user support pivot pivotally connects the user support to the main frame. A connecting link is movably associated with the user engagement device or exercise arm and at least one of the main frame, user support, or user support pivot. A user-activated positioning device controls positioning of the exercise arm in an exercise ready position at the start of an exercise. The user support pivot is positioned so that part of the combined weight of the user and user support is positioned on both sides of the gravitational centerline throughout the exercise movement and a portion of the combined weight passes through the centerline to redistribute the weight as the exercise arm is moved.