In this work, we examine the chemical composition of dust observed by the Chemistry Camera (ChemCam) instrument onboard the Mars Science Laboratory (MSL) rover at Gale Crater. The Laser Induced Breakdown Spectroscopy technique analyses samples without preparation, which allows detection of the elemental composition of surface deposits. Mars aeolian fine dust (<2-3 microns) composition is analyzed on the first shot of each Mars target. It is reproducible over time and present a composition characteristic of the global martian fine dust, which covers the entire planet and contributes to the local geology analyzed by MSL. Its composition can also be retrieved on the ChemCam Calibration Targets (CCCT) by subtraction of the well characterized CCCT spectra. The CCCT include eight glasses and ceramics that have been generated to simulate Martian rocks of interest and two targets of a single element (graphite for carbon and an alloy of titanium). ChemCam passive spectroscopy also indicates varying deposition of the dust cover on the CCCT.Major elements are quantified and shown to be very similar to the fine soils encountered at Gale crater. The composition is also similar to the soils and fine dust measured by APXS for the elements common to both instruments. The minor elements quantified by ChemCam (Ba, Sr, Rb, Li, Mn, Cr) are within the range of soil surveys, but we see a higher concentration of Li than in other types of remotely characterized targets. Sulfur is possibly detected at the ChemCam limit of detection. Hydrogen is clearly identified, indicating that this fine dust is a contributor to the H content of the martian soils, as also detected by the SAM and CheMin instruments, and provides constraints as to which fraction of the Martian surface is hydrated and altered. In conclusion, the finest fraction of dust particles on the surface of Mars contains hydrated components mixed intimately within the fine aeolian dust fraction, suggesting that this dust likely originates from mechanical weathering of altered grains.