  We propose a model-independent way to determine the cosmic curvature using
the Hubble parameter $H(z)$ measured with cosmic chronometers and the comoving
distance $D(z)$ inferred from HII galaxies. We employ Gaussian processes to
smooth the measure of distance and match it to $30$ values of $H(z)$. The
curvature parameter $\Omega_k$ may be obtained individually for each such pair.
The weighted average for the complete sample is $\Omega_k=-0.0013\pm0.0004$,
suggesting a bias towards negative values. The accuracy of the curvature
measurement improves with increased redshift, however, given possible
systematic effects associated with local inhomogeneities. We therefore also
analyze a high-redshift ($z>1.5$) sub-sample on its own, which is more likely
to reflect the geometry of the Universe on large, smooth scales. We find for
this set of data that $\Omega_k=-0.0111\pm0.0416$, consistent with zero to
better than $1\sigma$. This result is in agreement with the spatially flat
universe inferred from the cosmic microwave background observations. We expect
this method to yield even tighter constraints on the curvature parameter with
future, more accurate observations of HII galaxies at high $z$.
