Singular solutions of the Euclidean field equations for the O(3) σ-model in two dimensions are found. These are analogues of the meron field configurations that exist in four-dimensional gauge theories. Explicit multiple meron and anti-meron fields are constructed. It is shown that the long range meron-meron-anti-meron interactions are identical with those of a two-dimensional Coulomb gas. The geometrical meaning and the dynamics of the merons are discussed.