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Kim Kardashian and Kanye West chose a very unique name for baby #3 -- Chicago ... Kanye's hometown ... but it's a good bet she'll be known by a certain nickname.

Kim announced the name on her app by simply posting "Chicago West."

As we reported ... Kim and Kanye had their third child via surrogate, who gave birth Monday to a healthy girl weighing 7 lbs. 6 oz. Kim was in the delivery room during the birth, and we're told she was the first person to have skin-to-skin contact with the baby.

As you know, they already have 4-year-old North, and 2-year-old Saint. We're told the kids have been referring to her by the nickname Chi (pronounced Shy).