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Based on any chiral vertex operator algebra satisfying a suitable finitenesscondition, the semisimplicity of the zero-mode algebra as well as a regularityfor induced modules, we construct conformal field theory over the projectiveline with the chiral vertex operator algebra as symmetries of the theory. Weappropriately generalize the argument in [TUY] so that we are able to definesheaves of conformal blocks for chiral vertex operator algebras and study themin detail. We prove the factorization theorem under the fairly generalconditions for chiral vertex operator algebras and the zero-mode algebras.

Conformal field theories associated to regular chiral vertex operator algebras, I: Theories over the projective line