Kim Kardashian Pregnant -- Baby Conceived Near the Vatican

Kim Kardashian and Kanye West's pregnancy was far from an immaculate conception -- but it did go down in the shadow of the Vatican ... TMZ has learned.

Our Kim K. sources -- which are immaculate -- tell us the deed was done back in October ... during Kim and Kanye's romantic trip to Italy to celebrate Kim's 32nd birthday.

The couple was photographed all over Rome as they toured the Colosseum, the Sistine Chapel, and, of course ... the Pope's pad.

We're told Kim is about 12 weeks along ... so the math adds up.

One clue about how important that Italy trip is to Kim -- her blog lists it as #2 on her top 10 best moments of the year.