The one-dimensional linear convection-diffusion-(volumetric) reaction equation with a time-periodic velocity field is solved in a bounded region (0 less than x less than a), additionally incorporating surface chemical reaction into the boundary conditions imposed at the endpoints x equals 0, a. Floquet theory is used to construct a general solution of this initial- and boundary-value problem by expansion in time-periodic eigenfunctions phi //n(x, t). Eigenvalue problems for phi //n(x, t) and their adjoint counterparts psi //n(x, t) are formulated and studied. The eigenfunctions are shown to form complete biorthogonal sequences for any time t(0 less than t less than infinity ) in the functional space L//2 associated with the indicated spatial region. The Green's function for the pertinent inhomogeneous problem is constructed by a generalized finite Fourier transform method. The solution scheme may be used to analyze Taylor dispersion phenomena characterized by time-periodic local-space phenomenological coefficients.