  Small imines containing up to three carbon atoms are present in the
interstellar medium. As alkynyl compounds are abundant in this medium,
propargylimine thus represents a promising candidate for a new interstellar
detection. The goal of the present work is to perform a comprehensive
laboratory investigation of the rotational spectrum of propargylimine in its
ground vibrational state in order to obtain a highly precise set of
rest-frequencies and to search it in space. The rotational spectra of $E$ and
$Z$ geometrical isomers of propargylimine have been recorded in laboratory in
the 83-500 GHz frequency interval. The measurements have been performed using a
source-modulation millimetre-wave spectrometer equipped with a pyrolysis system
for the production of unstable species. High-level ab initio calculations were
performed to assist the analysis and to obtain reliable estimates for an
extended set of spectroscopic quantities. The improved spectral data allow us
to perform a successful search for this new imine in the quiescent
G+0.693-0.027 molecular cloud. Eighteen lines of $Z$-propargylimine have been
detected at level $>2.5 \sigma$, resulting in a column density estimate of $N =
(0.24\pm 0.02)\times 10^{14}$ cm$^{-2}$. An upper limit was retrieved for the
higher-energy $E$ isomer, which was not detected in the data. The fractional
abundance (w.r.t. H$_2$) derived for $Z$-propargylimine is $1.8\times
10^{-10}$. We discuss the possible formation routes by comparing the derived
abundance with those measured in the source for possible chemical precursors.
