Quantum entanglement enables tasks not possible in classical physics. Many quantum communication protocols require the distribution of entangled states between distant parties. Here, we experimentally demonstrate the successful transmission of an entangled photon pair over a 144km free-space link. The received entangled states have excellent, noise-limited fidelity, even though they are exposed to extreme attenuation dominated by turbulent atmospheric effects. The total channel loss of 64dB corresponds to the estimated attenuation regime for a two-photon satellite communication scenario. We confirm that the received two-photon states are still highly entangled by violating the Clauser-Horne-Shimony-Holt inequality by more than five standard deviations. From a fundamental point of view, our results show that the photons are subject to virtually no decoherence during their 0.5-ms-long flight through air, which is encouraging for future worldwide quantum communication scenarios.