The 34-year-old was asked about her newborn Charlotte during a Twitter Q&A through the Clinton Foundation this week.
Chelsea Clinton and Marc with baby Charlotte
"Congrats @ChelseaClinton on motherhood!" one fan wrote. "What are ways you're ensuring Charlotte & you are healthy in her first #1000 days? #MaternalHealth."
She replied, "@ThousandDays Ensuring we're both following drs' advice. Grateful 2 have this precious time w Charlotte & that she is a healthy baby!" She signed off, "CCM" – Chelsea Clinton Mezvinsky.
Chelsea and her investment banker husband Marc welcomed Charlotte on 26th September.
"Marc and I are full of love, awe and gratitude as we celebrate the birth of our daughter, Charlotte Clinton Mezvinsky," the proud mummy tweeted, before sharing a photo of her happy new family the following day.
At 7:03 PM on September 26th, we finally met Charlotte. We’re in love. pic.twitter.com/9ZCkoa6BPU— Chelsea Clinton (@ChelseaClinton) September 27, 2014
Charlotte is the first grandchild for Chelsea's parents, President Bill Clinton and former US Secretary of State Hillary Clinton.
"We are thrilled to be with our daughter and her husband as they welcome their daughter into the world," they said after her arrival. "Chelsea is well and glowing. Marc is bursting with pride. Charlotte's life is off to a good start."