Zeros of continuous-time linear periodic systems are defined and their properties investigated. Under the assumption that the system has uniform relative degree, the zero-dynamics of the system is characterized and a closed-form expression of the blocking inputs is derived. This leads to the definition of zeros as unobservable characteristic exponents of a suitably defined periodic pair. The zeros of periodic linear systems satisfy blocking properties that generalize the well-known time-invariant case. An efficient computational scheme is provided that essentially amounts to solving an eigenvalue problem. The new definition is finally used to characterize the zeros of systems described by input-output linear differential equations with periodic coefficients.