WASP-19b has the shortest orbital period of any known exoplanet, orbiting at
only 1.2 times the Roche tidal radius. By observing the Rossiter-McLaughlin
effect we show that WASP-19b's orbit is aligned, with lambda = 4.6 +/- 5.2
degrees. Using, in addition, a spectroscopic vsini and the observed rotation
period we conclude that the obliquity, psi, is less than 20 degrees. Further,
the eccentricity of the orbit is less than 0.02. We argue that hot Jupiters
with orbital periods as short as that of WASP-19b are two orders of magnitude
less common than hot Jupiters at the 3-4-d `pileup'. We discuss the evolution
of WASP-19b's orbit and argue that most likely it was first moved to near twice
the Roche limit by third-body interactions, and has since spiralled inwards to
its current location under tidal decay. This is compatible with a stellar
tidal-dissipation quality factor, Qs, of order 10^7.Comment: Version accepted for ApJ Letters (7 pages