We have measured the proper motion of the Draco dwarf galaxy using images at two epochs with a time baseline of about two years taken with the Hubble Space Telescope Advanced Camera for Surveys. Wide Field Channels 1 and 2 provide two adjacent fields, each containing a known QSO. The zero point for the proper motion is determined using both background galaxies and the QSOs and the two methods produce consistent measurements within each field. Averaging the results from the two fields gives a proper motion in the equatorial coordinate system of ({mu}_{alpha}_,{mu}_{delta}_)=(-17.7+/-6.3,-22.1+/-6.3)mas/century and in the Galactic coordinate system of ({mu}_l_,{mu}_b_)=(-23.1+/-6.3,-16.3+/-6.3)mas/century. Removing the contributions of the motion of the Sun and of the LSR to the measured proper motion yields a Galactic rest-frame proper motion of ({mu}_{alpha}_^Grf^,({mu}_{delta}_^Grf^)=(51.4+/-6.3,-18.7+/-6.3)mas/century and ({mu}_l_^Grf^,({mu}_b_^Grf^)=(-21.8+/-6.3,-50.1+/-6.3)mas/century. The implied space velocity with respect to the Galactic center is ({Pi},{Theta},Z)=27+/-14,89+/-25,-212+/-20)km/s. This velocity implies that the orbital inclination is 70{deg}, with a 95% confidence interval of (59{deg},80{deg}), and that the plane of the orbit is consistent with that of the vast polar structure (VPOS) of Galactic satellite galaxies.