Carbon-enhanced metal-poor (CEMP) stars bear important imprints of the early chemical enrichment of any stellar system. While these stars are known to exist in copious amounts in the Milky Way halo, detailed chemical abundance data from the faint dwarf spheroidal (dSph) satellites are still sparse, although the relative fraction of these stars increases with decreasing metallicity. Here, we report the abundance analysis of a metal-poor ([Fe/H]=$-2.5$ dex), carbon-rich ([C/Fe]=1.4 dex) star, ALW-8, in the Carina dSph using high-resolution spectroscopy obtained with the ESO/UVES instrument. Its spectrum does not indicate any over-enhancements of neutron capture elements. Thus classified as a CEMP-no star, this is the first detection of this kind of star in Carina. Another of our sample stars, ALW-1, is shown to be a CEMP-$s$ star, but its immediate binarity prompted us to discard it from a detailed analysis. The majority of the 18 chemical elements we measured are typical of Carinas field star population and also agree with CEMP stars in other dSph galaxies. Similar to the only known CEMP-no star in the Sculptor dSph and the weak-$r$-process star HD 122563, the lack of any strong barium-enhancement is accompanied by a moderate overabundance in yttrium, indicating a weak $r$-process activity. The overall abundance pattern confirms that, also in Carina, the formation site for CEMP-no stars has been affected by both faint supernovae and by standard core collapse supernovae. Whichever process was responsible for the heavy element production in ALW-8 must be a ubiquitous source to pollute the CEMP-no stars, acting independently of the environment such as in the Galactic halo or in dSphs.
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