FIG. 1 is a perspective view of the design of the present invention for a boutique chair; FIG. 2 is a front elevation view of the boutique chair in FIG. 1; FIG. 3 is a rear elevation view of the boutique chair in FIG. 1; FIG. 4 is a right side elevation view of the boutique chair in FIG. 1, the left side being a mirror image; and, FIG. 5 is a top end view of the boutique chair in FIG. 1.