A Differential RR Lyrae Line-of-Sight Distance Between M31 and M33

We present a purely differential line-of-sight distance between M31 and M33 using ab-type RR Lyrae variables observed in each galaxy by the Hubble Space Telescope Advanced Camera for Surveys in the F606W filter. Using 1501 RR Lyraes in 13 M31 fields and 181 RR Lyraes in six M33 fields, and placing all of these stars on a uniform photometric scale with internally consistent corrections for metal abundance and extinction, we find a relative absolute distance modulus of D(m-M)o = -0.298 +/- 0.016 in the sense of (m-M){o,M31} - (m-M)_{o,M33}. Adopting an absolute distance modulus of (m-M)_o=24.46 +/- 0.10 for M31 places M33 115 kpc beyond M31 in line-of-sight distance.