Exact solutions of heterotic string theory corresponding to four-dimensional magnetic black holes in N =4 supergravity are described. The solutions describe the black holes in the throat limit, and consist of a tensor product of an SU(2) WZW orbifold with the linear dilaton vacuum supersymmetrized to (1,0) world sheet SUSY. One dimension of the SU(2) model is interpreted as a compactified fifth dimension, leading to a four-dimensional solution with a Kaluza-Klein gauge field having a magnetic monopole background; this corresponds to a solution in N = 4 supergravity, since that theory is obtained by dimensional reduction of string theory.