Spring temperatures in temperate regions have increased over the past 20 years, and many organisms have responded to this increase by advancing the date of their growth and reproduction. Here we show that adaptation to climate change in a long-distance migrant is constrained by the timing of its migratory journey. For long-distance migrants climate change may advance the phenology of their breeding areas, but the timing of some species' spring migration relies on endogenous rhythms that are not affected by climate change. Thus, the spring migration of these species will not advance even though they need to arrive earlier on their breeding grounds to breed at the appropriate time. We show that the migratory pied flycatcher Ficedula hypoleuca has advanced its laying date over the past 20 years. This temporal shift has been insufficient, however, as indicated by increased selection for earlier breeding over the same period. The shift is hampered by its spring arrival date, which has not advanced. Some of the numerous long-distance migrants will suffer from climate change, because either their migration strategy is unaffected by climate change, or the climate in breeding and wintering areas are changing at different speeds, preventing adequate adaptation.