This is a report on a joint work in progress with Henri Darmon. Trying to generalize modular units in the setting of Hilbert modular forms, we are led to formulate a refinement of Stark's conjecture based on complex periods of Eisenstein series. First, I will recall some basic facts on special value of L-series at s=0, and explain why our construction is natural enough. Second, I will try to give convincing evidence, both theoretical and numerical, to support our conjecture.