Above the Sun's luminous photosphere lies the solar chromosphere, where the temperature increases from below 4000 K to over 1 million K. Though physicists do not understand the origin of these increases, they know it powers the solar wind with enormous consequences for the entire solar system. This report describes a set of simulations and analytical theory showing that solar atmospheric flows originating in the photosphere will frequently drive a previously unidentified thermal plasma instability that rapidly develops into turbulence. Though this turbulence is small scale (centimeters to a few meters), it will modify the conductivity, temperatures, and energy flows through much of the chromosphere. Incorporating the effects of this turbulence, and other small-scale turbulence, into large-scale models of solar and stellar atmospheres will improve physicists' ability to model energy flows with important consequences for the predicted temperatures and radiation patterns.