  Let $(\varphi_\alpha,\xi_\alpha,g)$ for $\alpha=1,2$, and $3$ be a contact
metric $3$-structure on the manifold $M^{4n+3}$. We show that the $3$-contact
distribution of this structure admits a HyperKahler structure whenever
$(M^{4n+3},\varphi_\alpha,\xi_\alpha,g)$ is a $3$-Sasakian manifold. In this
case, we call it HyperKahler contact distribution. To analyze the curvature
properties of this distribution, we define a special metric connection that is
completely determined by the HyperKahler contact distribution. We prove that
the $3$-Sasakian manifold is of constant $\varphi_{\alpha}$-sectional
curvatures if and only if its HyperKahler contact distribution has constant
holomorphic sectional curvatures.
