Chromium Ore is found below the Toxic Caverns. As you go deeper the richness of the veins will increase. It can be mined by the Build Gun MK3, the Hard Rock Grinder and Trencher Extractors.
The first stages of Ore smelting can be done with standard Ore Smelters. Chromium Ore requires the "Arc Smelter" upgrade to be processed by Ore Smelters as it requires higher melting temperatures than normal. Later, when throughput is valued over efficiency, a Blast Furnace setup is strongly recommended.