  With ultracold $^{87}$Sr confined in a magic wavelength optical lattice, we
present the most precise study (2.8 Hz statistical uncertainty) to-date of the
$^1S_0$ - $^3P_0$ optical clock transition with a detailed analysis of
systematic shifts (20 Hz uncertainty) in the absolute frequency measurement of
429 228 004 229 867 Hz. The high resolution permits an investigation of the
optical lattice motional sideband structure. The local oscillator for this
optical atomic clock is a stable diode laser with its Hz-level linewidth
characterized across the optical spectrum using a femtosecond frequency comb.
