  We present the first detection of the l-C3H+ hydrocarbon in the interstellar
medium. The Horsehead WHISPER project, a millimeter unbiased line survey at two
positions, namely the photo-dissociation region (PDR) and the nearby shielded
core, revealed a consistent set of eight unidentified lines toward the PDR
position. Six of them are detected with a signal-to-noise ratio from 6 to 19,
while the two last ones are tentatively detected. Mostly noise appears at the
same frequency toward the dense core, located less than 40" away. We
simultaneously fit 1) the rotational and centrifugal distortion constants of a
linear rotor, and 2) the Gaussian line shapes located at the eight predicted
frequencies. The observed lines can be accurately fitted with a linear rotor
model, implying a 1Sigma ground electronic state. The deduced rotational
constant value is Be= 11244.9512 +/- 0.0015 MHz, close to that of l-C3H. We
thus associate the lines to the l-C3H+ hydrocarbon cation, which enables us to
constrain the chemistry of small hydrocarbons. A rotational diagram is then
used to infer the excitation temperature and the column density. We finally
compare the abundance to the results of the Meudon PDR photochemical model.
