Kelsey Grammer, wife Kayte welcome baby girl

By Ann Oldenburg, USA TODAY

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Kelsey and Kayte Grammer renew their wedding vows at the Little Church of the West after one year of marriage on June 2 in Las Vegas. (Credit: By Denise Truscello, WireImage)

Congrats to the Grammers!

Kelsey Grammer's wife, Kayte, delivered "a healthy baby girl" this morning at 1 a.m. in Los Angeles, the star's rep, Stan Rosenfield, tells Lifeline Live.

The couple named her Faith Evangeline Elisa Grammer, and she's the first child for Kelsey and Kayte, who got married in February 2011. They renewed their vows last month in Las Vegas. The baby weighed in at 6 lbs., 2 oz.

Little Faith was almost born in Chicago. The Grammers returned to Los Angeles yesterday from Chicago, after Kelsey completed filming the second season of his Starz series, Boss.

In a personal note from Kayte and Kelsey, 57, the two say that, "Mother and child are in excellent health." They also explain:

"We were ecstatic earlier this year, when we announced that Kayte was carrying twins. Tragically we lost the little boy shortly thereafter. This was not something we cared to make known publicly at the time. It was unspeakably painful and we know that people will understand our desire to keep the news private then, as we know they will respect our privacy in this matter now.

"A glorious birth with a lingering sadness is ours today. We choose to celebrate the life that has been given us. We proudly introduce our Faith to the world today looking forward to the days ahead and the children yet to come."