There is a simple answer: Botticelli's Chart of Hell, painted in the fifteenth century, is now in the Biblioteca Apostolica Vaticana (Vatican Library).
While it is true that the "map" was not painted by Dante himself, Dante was the inspiration for Botticelli's painting of it. Therefore, Botticelli's painting is his original. He's the one who painted Chart of Hell.
Asked and answered. There is no reason to doubt this in any logical sense, nor is there any reason to "interpret" LucidElement's question beyond common sense. If this discussion exists now only to bicker and sling names at one another, I will shortly be tempted to lock it.