The Zika virus (ZIKV) spread rapidly in Brazil in 2015 and 2016. Rio de Janeiro was among the Brazilian cities which were hit the hardest, with more that a hundred thousand confirmed cases up to the end of 2016. Given the severity of the neurological damage caused by ZIKV on fetuses, we wondered whether it would also cause an increase in the number of miscarriages, especially very early ones. As early miscarriages are unlikely to be recorded as a health event, this effect — if it occurred — would only show up as a reduction in the number of live births. In this paper we show that there was a 15% drop in live births between September and December 2016 compared to the previous year, and that this sharp drop from epidemiological week 33 onward is strongly correlated with the number of recorded cases of Zika about 40 weeks earlier. We postulate that ZIKV is directly responsible for this drop in the birth rate. Further work is required to ascertain whether other factors such the fear of having a microcephaly baby or the economic crisis are having a significant effect.