  The partially deuterated linear isomer HDCCC of the ubiquitous cyclic carbene
($c$-C$_3$H$_2$) was observed in the starless cores TMC-1C and L1544 at 96.9
GHz, and a confirming line was observed in TMC-1 at 19.38 GHz. To aid the
identification in these narrow line sources, four centimetre-wave rotational
transitions (two in the previously reported $K_a =0$ ladder, and two new ones
in the $K_a =1$ ladder), and 23 transitions in the millimetre band between 96
and 272 GHz were measured in high-resolution laboratory spectra. Nine
spectroscopic constants in a standard asymmetric top Hamiltonian allow the
principal transitions of astronomical interest in the $K_a \le 3$ rotational
ladders to be calculated to within 0.1 km s$^{-1}$ in radial velocity up to 400
GHz. Conclusive evidence for the identification of the two astronomical lines
of HDCCC was provided by the $V_{\rm{LSR}}$ which is the same as that of the
normal isotopic species (H$_2$CCC) in the three narrow line sources. In these
sources, deuterium fractionation in singly substituted H$_2$CCC (HDCCC/H$_2$CCC
$\sim4\%\text{-}19\%$) is comparable to that in $c$-C$_3$H$_2$
($c$-C$_3$H$_2$/$c$-C$_3$HD $\sim5\%\text{-}17\%$), and similarly in doubly
deuterated $c$-C$_3$H$_2$ ($c$-C$_3$D$_2$/$c$-C$_3$HD $\sim3\%\text{-}17\%$),
implying that the efficiency of the deuteration processes in the H$_2$CCC and
$c$-C$_3$H$_2$ isomers are comparable in dark clouds.
