  Based on a novel laboratory method, 14 mm-wave lines of the molecular ion
H$_2$CCCH$^+$ have been measured in high resolution, and the spectroscopic
constants of this asymmetric rotor determined with high accuracy. Using the
Yebes 40 m and IRAM 30 m radio telescopes, we detect four lines of
H$_2$CCCH$^+$ towards the cold dense core TMC-1. With a dipole moment of about
0.55 Debye obtained from high-level ab initio calculations, we derive a column
density of 5.4$\pm$1$\times$10$^{11}$ cm$^{-2}$ and
1.6$\pm$0.5$\times$10$^{11}$ cm$^{-2}$ for the ortho and para species,
respectively, and an abundance ratio N(H$_2$CCC)/N(H$_2$CCCH$^+$)= 2.8$\pm$0.7.
The chemistry of H$_2$CCCH$^+$ is modelled using the most recent chemical
network for the reactions involving the formation of H$_2$CCCH$^+$. We find a
reasonable agreement between model predictions and observations, and new
insights into the chemistry of C$_3$ bearing species in TMC-1 are obtained.
