  The doubly Cabibbo-suppressed decay $\Xi_{c}^{+}\to p\phi$ with $\phi\to
K^{+}K^{-}$ is observed for the first time, with a statistical significance of
more than fifteen standard deviations. The data sample used in this analysis
corresponds to an integrated luminosity of 2 fb$^{-1}$ recorded with the LHCb
detector in $pp$ collisions at a centre-of-mass energy of 8 TeV. The ratio of
branching fractions between the decay $\Xi_{c}^{+}\to p\phi$ and the singly
Cabibbo-suppressed decay $\Xi_{c}^{+}\to pK^{-}\pi^{+}$ is measured to be
\begin{equation*} \frac{\mathcal{B}(\Xi_{c}^{+}\to
p\phi)}{\mathcal{B}(\Xi_{c}^{+}\to pK^{-}\pi^{+})} = (19.8 \pm 0.7 \pm 0.9 \pm
0.2) \times 10^{-3}, \end{equation*} where the first uncertainty is
statistical, the second systematic and the third due to the knowledge of the
$\phi\to K^{+}K^{-}$ branching fraction.
