The first approximately 600 million years of Earth history (the 'Hadean' eon) remain poorly understood, largely because there is no rock record dating from that era. Detrital Hadean igneous zircons from the Jack Hills, Western Australia, however, can potentially provide insights into the conditions extant on our planet at that time. Results of geochemical investigations using these ancient grains have been interpreted to suggest the presence of a hydrosphere and continental crust before 4 Gyr. An underexploited characteristic of the >4 Gyr zircons is their diverse assemblage of mineral inclusions. Here we present an examination of over 400 Hadean zircons from Jack Hills, which shows that some inclusion assemblages are conducive to thermobarometry. Our thermobarometric analyses of 4.02-4.19-Gyr-old inclusion-bearing zircons constrain their magmatic formation conditions to about 700 degrees C and 7 kbar. This result implies a near-surface heat flow of approximately 75 mW m(-2), about three to five times lower than estimates of Hadean global heat flow. As the only site of magmatism on modern Earth that is characterized by heat flow of about one-quarter of the global average is above subduction zones, we suggest that the magmas from which the Jack Hills Hadean zircons crystallized were formed largely in an underthrust environment, perhaps similar to modern convergent margins.