The ratio of permanent residents to churches on Antarctica is 500:1 in the summer and about 120:1 during the winter. The US ratio is about 900:1.
Antarctica has proportionally more churches than America. And half are Roman Catholic, three are Orthodox, one is Protestant (this is like a 4th grade math problem, how many are there? but to be fair, the interdenominational Protestant one is the oldest).
As of 2015, Moscow had about 20000 persons per church. The “Build 200 Churches” program (that had some wags worried about overbuilding…) would leave the ratio at 15000 persons per church, still a long way from the US or Antarctica.
As an interesting tangent, upper estimates for Christianity in China report perhaps 1:10 to 1:20 persons as Christian. If a house church averages 20-40 people (a total guess), that would put the population:church ratio at about 200-800 : 1 – possibly better than the US.
Anyhow, if I had grabbed a population-per-church number out of the air, it would probably be close to 1000:1, which fits the US. I would not have guessed that Antarctica was way out front. (No data on attendance, though.)
But the annual-average winner (in my very limited survey of the internets):
Vatican City. 120:1. (All Catholic, of course…)