The successful isolation of graphene ten years ago has evoked a rapidly growing scientific interest in the nature of two-dimensional (2D) crystals. A number of different 2D crystals has been produced since then, with properties ranging from superconductivity to insulating behavior. Here, we predict the possibility for realizing ferromagnetic 2D crystals by exfoliating atomically thin films of K2CuF4. From a first-principles theoretical analysis, we find that single layers of K2CuF4 form exactly 2D Kosterlitz-Thouless systems. The 2D crystal can form a free-standing membrane, and exhibits an experimentally accessible transition temperature and robust magnetic moments of 1 mu(B) per formula unit. 2D K2CuF4 unites ferromagnetic and insulating properties and is a demonstration of principles for nanoelectronics such as novel 2D-based heterostructures.