I don't know who first asked this question, but it's a question that I think many differential and complex geometers have tried to answer because it sounds so simple and fundamental. There are even a number of published proofs that are not taken seriously, even though nobody seems to know exactly why they are wrong.
The latest published proof to the affirmative: http://arxiv.org/abs/math/0505634 Even though the preprint is old it was just published in Journ. Math. Phys. 56, 043508-1-043508-21 (2015)
