If neutrinos get mass via the seesaw mechanism the mixing matrix describing neutrino oscillations can be effectively nonunitary. We show that in this case the neutrino appearance probabilities involve a new CP phase ϕ associated with nonunitarity. This leads to an ambiguity in extracting the "standard" three-neutrino phase δ_{CP}, which can survive even after neutrino and antineutrino channels are combined. Its existence should be taken into account in the planning of any oscillation experiment aiming at a robust measurement of δ_{CP}.