Searches for very-high-redshift galaxies over the past decade have yielded a large sample of more than 6,000 galaxies existing just 900-2,000 million years (Myr) after the Big Bang (redshifts 6 > z > 3; ref. 1). The Hubble Ultra Deep Field (HUDF09) data(2,3) have yielded the first reliable detections of z approximate to 8 galaxies(3-9) that, together with reports of a c-ray burst at z approximate to 8.2 (refs 10, 11), constitute the earliest objects reliably reported to date. Observations of z approximate to 7-8 galaxies suggest substantial star formation at z > 9-10 (refs 12, 13). Here we use the full two-year HUDF09 data to conduct an ultra-deep search for z approximate to 10 galaxies in the heart of the reionization epoch, only 500 Myr after the Big Bang. Not only do we find one possible z approximate to 10 galaxy candidate, but we show that, regardless of source detections, the star formation rate density is much smaller (similar to 10%) at this time than it is just similar to 200 Myr later at z approximate to 8. This demonstrates how rapid galaxy build-up was at z approximate to 10, as galaxies increased in both luminosity density and volume density from z approximate to 10 to z approximate to 8. The 100-200 Myr before z approximate to 10 is clearly a crucial phase in the assembly of the earliest galaxies.