  We present a method for measuring the Hubble parameter, H(z), and angular
diameter distance, D_A(z), from the two-dimensional two-point correlation
function, and validate it using LasDamas mock galaxy catalogs. Applying our
method to the sample of luminous red galaxies (LRGs) from the Sloan Digital Sky
Survey (SDSS) Data Release 7 (DR7), we measure H(z=0.35)=82.1_{-4.9}^{+4.8} km
s^{-1}Mpc^{-1}, D_A(z=0.35)=1048_{-58}^{+60} Mpc without assuming a dark energy
model or a flat Universe. We find that the derived measurements of
H(0.35)r_s(z_d)/c and D_A(0.35)/r_s(z_d) (where r_s(z_d) is the sound horizon
at the drag epoch) are nearly uncorrelated, have tighter constraints and are
more robust with respect to possible systematic effects. Our galaxy clustering
measurements of {H(0.35)r_s(z_d)/c, D_A(0.35)/r_s(z_d)}={0.0434\pm
0.0018,6.60\pm 0.26} (with the correlation coefficient r = 0.0604) can be used
to combine with cosmic microwave background and any other cosmological data
sets to constrain dark energy. Our results represent the first measurements of
H(z) and D_A(z) (or H(z)r_s(z_d)/c and D_A(0.35)/r_s(z_d)) from galaxy
clustering data. Our work has significant implications for future surveys in
establishing the feasibility of measuring both H(z) and D_A(z) from galaxy
clustering data.
