FIG. 1 is a front view of a dental handpiece showing my new design; FIG. 2 is a right side view of the dental handpiece of FIG. 1; FIG. 3 is a left side view of the dental handpiece of FIG. 1; FIG. 4 is a top plan view of the dental handpiece of FIG. 1; FIG. 5 is a bottom view of the dental handpiece of FIG. 1; and, FIG. 6 is a perspective view of the dental handpiece of FIG. 1.