  The rotational spectrum of silyl isocyanide (SiH$_3$NC), an isomer of the
well studied silyl cyanide (SiH$_3$CN), has been detected in the laboratory in
a supersonic molecular beam, and the identification was confirmed by
observations of the corresponding rotational transitions in the rare isotopic
species SiH$_3$$^{15}$NC and SiH$_3$N$^{13}$C. Spectroscopic constants derived
from 19 transitions between $11 - 35$~GHz in the three lowest harmonically
related rotational transitions in the $K = 0 ~{\rm{and}}~1$ ladders of the
normal isotopic species including the nitrogen nuclear quadrupole hyperfine
constant, allow the principal astronomical transitions of SiH$_3$NC to be
calculated to an uncertainty of about 4~km~s$^{-1}$ in equivalent radial
velocity, or within the FWHM of narrow spectral features in the inner region of
IRC+10216 near 200~GHz. The concentration of SiH$_3$NC in our molecular beam is
three times less than SiH$_3$CN, or about the same as the corresponding ratio
of the isomeric pair SiNC and SiCN produced under similar conditions. Silyl
isocyanide is an excellent candidate for astronomical detection, because the
spectroscopic and chemical properties are very similar to SiH$_3$CN which was
recently identified in the circumstellar envelope of IRC+10216 by
\citet{cernicharo_discovery_2017} and of SiNC and SiCN in the same source.
