  This is the first of the two papers devoted to the study of global regularity
of the 3+1 dimensional Einstein-Klein-Gordon system with a $U(1)\times
\mathbb{R}$ isometry group. In this first part, we reduce the Cauchy problem of
the Einstein-Klein-Gordon system to a 2+1 dimensional system. Then, we will
give energy estimates and construct the null coordinate system, under which we
finally show that the first possible singularity can only occur at the axis.
