While the high-z frontier of star formation rate (SFR) studies has advanced rapidly, direct measurements beyond z ~ 4 remain difficult, as shown by significant disagreements among different results. Gamma-ray bursts, owing to their brightness and association with massive stars, offer hope of clarifying this situation, provided that the GRB rate can be properly related to the SFR. The Swift GRB data reveal an increasing evolution in the GRB rate relative to the SFR at intermediate z; taking this into account, we use the highest-z GRB data to make a new determination of the SFR at z = 4-7. Our results exceed the lowest direct SFR measurements and imply that no steep drop exists in the SFR up to at least z ~ 6.5. We discuss the implications of our result for cosmic reionization, the efficiency of the universe in producing stellar-mass black holes, and "GRB feedback" in star-forming hosts.