  We present new spectroscopic and photometric observations of the HAT-P-1
planetary system. Spectra obtained during three transits exhibit the
Rossiter-McLaughlin effect, allowing us to measure the angle between the sky
projections of the stellar spin axis and orbit normal, \lambda = 3.7 +/- 2.1
degrees. The small value of \lambda for this and other systems suggests that
the dominant planet migration mechanism preserves spin-orbit alignment. Using
two new transit light curves, we refine the transit ephemeris and reduce the
uncertainty in the orbital period by an order of magnitude. We find a upper
limit on the orbital eccentricity of 0.067, with 99% confidence, by combining
our new radial-velocity measurements with those obtained previously.
