We develop a formulation of conformal field theory on multiply connected domains and establish its connection to the theory of SLE. Within this framework, we derive the Eguchi-Ooguri version of Ward equations, which express stress-tensor insertions via Lie derivatives and differential operators that depend on Teichmüller modular parameters. Additionally, we present a conformal field-theoretic construction of SLE in multiply connected domains and a class of martingale observables for this process.