  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,
$f(z)\sigma_8(z)=0.482\pm 0.116$ at $z\sim 1.4$ after marginalizing over the
galaxy bias parameter $b(z)\sigma_8(z)$. This corresponds to $4.2\sigma$
detection of RSD. Our constraint is consistent with the prediction of general
relativity $f\sigma_8\sim 0.392$ within the $1-\sigma$ confidence level. When
we allow $\sigma_{\rm v}$ to vary and marginalize it over, the growth rate
constraint becomes $f\sigma_8=0.494^{+0.126}_{-0.120}$. We also demonstrate
that by combining with the low-z constraints on $f\sigma_8$, high-z galaxy
surveys like the FastSound can be useful to distinguish modified gravity models
without relying on CMB anisotropy experiments.
