  V606 Centauri (V606 Cen) is an early B-type close binary with an orbital
period of 1.4950935\,d and the complete light curves are very difficult to be
observed on the ground. By analyzing the unbroken and continuous light curve
obtained by TESS, we found that it is a marginal contact binary with a very low
fill-out factor of about 2\%. The O-C diagram of V606 Cen is constructed for
the first time based on the 118.8-years eclipse times. It is found that the O-C
diagram shows a downward parabolic change together with a cyclic oscillation
with an amplitude of 0.0544\, d and a period of 88.8\, yr. The downward
parabolic variation reveals a linear period decrease at a rate of $dP/dt =
-2.06 \times{10^{-7}} d \cdot yr^{-1}$ that can be explained by the mass
transfer from the more massive component to the less massive one. Both the
marginal contact configuration and the continuous period decrease suggest that
V606 Cen is a newly formed contact binary via Case A mass transfer. Meanwhile,
the cyclic change in the O-C diagram can be explained by the Light-Travel Time
Effect via the presence of a third body. The lowest mass of the tertiary
companion is determined as M$_{3}$ = 4.51($\pm0.38$)M$_{\odot}$ that is
orbiting around the central eclipsing binary in a nearly circular orbit
(e=0.32). All the results indicate that V606 Cen is a newly formed massive
contact binary and just reaches the contact configuration during the mass
transfer in a hierarchical triple system.
