  We report the detection of orbital decay in the 12.75-min, detached binary
white dwarf (WD) SDSS J065133.338+284423.37 (hereafter J0651). Our photometric
observations over a 13-month baseline constrain the orbital period to
765.206543(55) s and indicate the orbit is decreasing as a rate of (-9.8 +/-
2.8) x 10^(-12) s/s (or -0.31 +/- 0.09 ms/yr). We revise the system parameters
based on our new photometric and spectroscopic observations: J0651 contains two
WDs with M1 = 0.26 +/- 0.04 Msun and M2 = 0.50 +/- 0.04 Msun. General
relativity predicts orbital decay due to gravitational wave radiation of (-8.2
+/- 1.7) x 10^(-12) s/s (or -0.26 +/- 0.05 ms/yr). Our observed rate of orbital
decay is consistent with this expectation. J0651 is currently the
second-loudest gravitational wave source known in the milli-Hertz range and the
loudest non-interacting binary, which makes it an excellent verification source
for future missions aimed at directly detecting gravitational waves. Our work
establishes the feasibility of monitoring this system's orbital period decay at
optical wavelengths.
