In plane Couette flow a fully nonlinear time-periodic solution to the incompressible Navier-Stokes equations and its stable manifold have recently been found to form the basin boundary between laminar and turbulent flows [Kawahara, Phys. Fluids 17, 041702 (2005)]. Here we present homoclinic orbits from/to this edge-state periodic solution [van Veen & Kawahara, Phys. Rev. Lett. 107, 114501 (2011)]. Through the Smale-Birkhoff theorem their existence may explain transient turbulence. The homoclinic orbits are then traced down to the onset Reynolds number of homoclinic tangle leading to transient turbulence. The appearance of transient turbulence is considered to be a consequence of boundary crisis of a chaotic attractor on the periodic edge state.