Hall algebras of categories of quiver representations and coherent sheaves on smooth projective curves over $F_q$ recover interesting representation-theoretic objects such as quantum groups and their generalizations. I will define and describe the structure of the Hall algebra of coherent sheaves on a projective variety over $F_1$, with $P^2$ as the main example. Examples suggest that it should be viewed as a degenerate $q\to 1$ limit of its counterpart over $F_q$.