  In this paper, the HyperKahler contact distribution of a 3-Sasakian manifold
is studied. To analyze the curvature properties of this distribution, the
special metric connection $\bar{\nabla}$ is defined. This metric connection is
completely determined by HyperKahler contact distribution. We prove that
HyperKahler contact distribution is of constant holomorphic sectional
curvatures if and only if its 3-Sasakian manifold is of constant
$\varphi_{\alpha}$-sectional curvatures. Moreover, it is shown that there is an
interesting relation between the sectional curvatures of
$\varphi_{\alpha}$-planes on $TM$ of metric connection $\bar{\nabla}$ and the
Levi-Civita connection.
