Kim Kardashian & Kanye West's 3rd Baby Due in January

Kim Kardashian and Kanye West will expand their brood by 1 come Winter.

We're told baby #3 is due at the end of January.

TMZ broke the story, Kim and Kanye hired a surrogate because she has a medical condition -- placenta accreta -- that became extremely serious during her second pregnancy and we're told it could become life-threatening if she tried to carry another baby to term.

They paid $45k for the surrogate, who is prohibited from smoking, drinking or doing drugs during the pregnancy. Also, no hot tubs, hair dye and raw fish.

We're told so far, so good.