We measure the redshift-space correlation function from a spectroscopic sample of 2783 emission line galaxies from the FastSound survey. The survey, which uses the Subaru Telescope and covers the redshift ranges of $1.19<z<1.55$, is the first cosmological study at such high redshifts. We detect clear anisotropy due to redshift-space distortions (RSD) both in the correlation function as a function of separations parallel and perpendicular to the line of sight and its quadrupole moment. RSD has been extensively used to test general relativity on cosmological scales at $z<1$. Adopting a LCDM cosmology with the fixed expansion history and no velocity dispersion $sigma_{rm v}=0$, and using the RSD measurements on scales above 8Mpc/h, we obtain the first constraint on the growth rate at the redshift, $f(z)sigma_8(z)=0.482pm 0.116$ at $zsim 1.4$ after marginalizing over the galaxy bias parameter $b(z)sigma_8(z)$. This corresponds to $4.2sigma$ detection of RSD. Our constraint is consistent with the prediction of general relativity $fsigma_8sim 0.392$ within the $1-sigma$ confidence level. When we allow $sigma_{rm v}$ to vary and marginalize it over, the growth rate constraint becomes $fsigma_8=0.494^{+0.126}_{-0.120}$. We also demonstrate that by combining with the low-z constraints on $fsigma_8$, high-z galaxy surveys like the FastSound can be useful to distinguish modified gravity models without relying on CMB anisotropy experiments.
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