In 1855, James Clerk Maxwell first proposed the concept of combining three separate single-color exposures into one image to create a full-color photograph, but it wasn't until 1861 that he managed to do so, with the help of photographer Thomas Sutton — the inventor of the single lens reflex camera. The pair took three seperate exposures of a tartan ribbon, each through a different color filter — red, green and blue. On May 17th of that year, at a Royal Institution lecture on colour theory, the slides were then each projected through that same color filtered lens, and focused and combined into a single, full-color image.
Clerk Maxwell had discovered the idea when researching color vision, when he discovered that of all the cones in the human eye, some are more sensitive to red, others green and others blue — and from this he surmised that from the three we can create all the rest of colors — and so created modern color theory.
The first demonstration wasn't particularly succesful, as the red and green exposures weren't nearly sensitive enough to capture all the color in the tartan ribbon, but it was the first full-color image, and the basis of color photography as we know it.