The baby has been named Elle Cynthia Jordan.
Cindy became the surrogate for her grandchild after an in-vitro procedure that implanted an embryo made from her 32-year-old daughter Emily's egg and son-in-law Mike Jordan's sperm.
Emily was 29 when she was diagnosed with cervical cancer in 2010.
Devastatingly, just as she was about to have a radical hysterectomy, Emily and husband Mike discovered she was pregnant.
Faced with saving her own life or their unborn child's, the couple made the excruciating decision to go forward with her surgery. It meant losing the baby, and - they thought at the time - forfeiting any chance at having their own children.
Emily said: "I can't describe what that was like after finding out you have cancer, after finding out your chance of ever carrying a baby is gone."
But her mother Cindy brought fresh hope of a child when she offered to act as a surrogate.
When doctors revealed that they had been able to keep Emily's ovaries intact, she immediately offered to help. Initially Emily, who works in hospital administration, and Mike didn't take her offer seriously.
But Cindy, an executive director at a medical foundation in Chicago, was adamant.
The thought of Emily and Mike not being able to have children and share that piece of their lives with someone just broke my heart. I want Emily to have that connection with another human being like I had with her.
During the pregnancy, people started asking Cindy about 'her baby.' She was quick to correct them and reveal she was actually carrying her grandchild.
While admitting she was worried about the physical toll a pregnancy at her age might take, Cindy said her body handled it better than she expected.
She also wondered how well she'd recover from a Caesarean section. She'd had C-sections for Emily and her older son, but that had been three decades before.
Before the birth, Emily said: "This is a continuation of everything that she has done her entire life for me, which is to make sure that I have the best life possible."
Cindy added: "I know I gave a gift. But I'm also getting so much in return.'
Last week, a few days after Emily's 32nd birthday, mother and daughter were together in the delivery room in a Chicago hospital.
After their longed for daughter Elle Cynthia Jordan was born, Emily rushed out to show their newborn to Mike. "She looks just like you! She looks just like you!," she cried.
Cindy has even said she would consider doing it again for a sibling for Elle.
She added: "When I watch both of them hold that baby and look into her face, it's like everything I could have imagined wanting for them - better than I could have imagined.
"This is what it was all about for me."
What an amazing woman to give such a gift to her daughter.
You can see the video interview of Cindy and Emily when Cindy was expecting her granddaughter here.
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