A model of chiral bosons on a non-commutative field space is constructed and new generalized bosonization (fermionization) rules for these fields are given. The conformal structure of the theory is characterized by a level of the Kac-Moody algebra equal to (1+ θ^2) where θ is the non-commutativity parameter and chiral bosons living in a non-commutative fields space are described by a rational conformal field theory with the central charge of the Virasoro algebra equal to 1. The non-commutative

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... hiral bosons are shown to correspond to a free fermion moving with a speed equal to c^' = c √(1+θ^2) where c is the speed of light. Lorentz invariance remains intact if c is rescaled by c → c^'. The dispersion relation for bosons and fermions, in this case, is given by ω = c^' | k|.