  We find a coordinate-independent wave-packet solution of the massive
Klein-Gordon equation with the conformal coupling to gravity in the de-Sitter
universe. This solution can locally be represented through the superposition of
positive-frequency plane waves at any space-time point, assuming that the
scalar-field mass $M$ is much bigger than the de-Sitter Hubble constant $H$.
The solution is also shown to be related to the two-point function in the
de-Sitter quantum vacuum. Moreover, we study the wave-packet propagation over
cosmological times, depending on the ratio of $M$ and $H$. In doing so, we find
that this wave packet propagates like a point-like particle of the same mass if
$M \ggg H$, but, if otherwise, the wave packet behaves highly non-classically.
