When immersed in liquid ³He, the nanometer strands of aerogel are coated with a thin layer of solid ³HE, forming a network of irregular nanotubes. Owing to its high purity and weak interactions, this system is ideal for studying fundamental processes. We report the first experiments on solid ³He in aerogel at ultralow temperatures, cooled by direct adiabatic demagnetization. Simultaneous nuclear magnetic susceptibility and heat capacity measurements indicate a magnetic phase transition.