Daughter for Chelsea Clinton (and Granddaughter for a Certain Couple)

By AMY CHOZICK and NICHOLAS KULISHSEPT. 27, 2014

Hillary Rodham Clinton and Bill Clinton with their granddaughter, Charlotte Clinton Mezvinsky. Credit Jon Davidson/Office of President Clinton

As late as Wednesday afternoon, Ms. Clinton was on stage delivering speeches and moderating panels at the Clinton Global Initiative gathering in New York.

The Clintons’ soon-to-arrive grandbaby was a constant topic of conversation at the meeting. When asked by CNN if he would “baby-proof” the White House — the implication being that Mrs. Clinton would not only run for president in 2016 but also win — Mr. Clinton replied, “One thing at a time.”

Chelsea Clinton and Marc Mezvinsky with their daughter, Charlotte Clinton Mezvinsky. Credit Jon Davidson/Office of President Clinton

Both Mr. and Mrs. Clinton have a packed schedule this fall to raise money and campaign for Democrats in the midterm elections, although by Saturday morning Mr. Clinton had canceled an evening fund-raising event in Denver for Senator Mark Udall and Gov. John W. Hickenlooper.

Ms. Clinton, 34, announced her pregnancy in April at an event on the Lower East Side of Manhattan, her mother at her side and her husband watching from the back of the room.

The baby arrives as the family, never out of the spotlight since Mr. Clinton was elected president in 1992, has moved center stage amid speculation that Mrs. Clinton will run for president, a decision that is considered likely but that she has remained coy about. She has said the baby’s arrival could be a factor in her decision.

“I’m about to have my first grandchild, which I’m thrilled about,” Mrs. Clinton told Charlie Rose on PBS in July. “I want to see what that feels like,” she added. “I’m not going to skip over it.”

Chelsea Clinton, the vice chairwoman of the Bill, Hillary & Chelsea Clinton Foundation, married Mr. Mezvinsky in 2010, and they live in New York.

Chelsea Clinton earlier this month. The baby was born on Friday, according to a Clinton spokesman. Credit Ray Stubblebine/European Pressphoto Agency

She has worked at a hedge fund and the consultant McKinsey & Company and holds degrees from Stanford, Columbia and Oxford. Last month, Ms. Clinton announced that she was leaving her position as a special correspondent for NBC News less than three years into a tenure at the network that was at times bumpy.

Ms. Clinton has been a national public figure since she was 12, when her father was elected to his first term in the White House. Her adolescence unfolded in highly public fashion, despite efforts by her parents to shield her from the publicity and scrutiny that any presidential child endures. They largely succeeded, but that was before the Internet had firmly taken root and when social media was in its infancy.

As she has grown into adulthood, Ms. Clinton has slowly become comfortable with the public attention. During the 2008 Democratic presidential primary, she campaigned on behalf of her mother. Her wedding to Mr. Mezvinsky in Rhinebeck, N.Y., drew onlookers, autograph seekers and a baseball team mascot dressed as a raccoon.

Those experiences, and the advice of her grandmother Dorothy Rodham, led Ms. Clinton to take a more public role in recent years, including the job at NBC and a leadership position at her family’s foundation.

Ms. Clinton frequently delivers talks for the foundation and occasionally delivers paid speeches for about $75,000 each. A spokesman said Ms. Clinton donated the money to the foundation.

On Tuesday, during a discussion about the campaign to end poaching of African elephants, Ms. Clinton said she worried that her first child could “grow up in a world without elephants.” The baby has an elephant-themed nursery at the couple’s apartment in the Flatiron district of Manhattan, keeping with the theme of one of Ms. Clinton’s primary charitable causes.

What kind of grandparents will Mr. and Mrs. Clinton be? Just days before the baby was born, the former president said he had to remind himself every day whose child this is. “Do not interfere! Be there when you’re welcome. Be loving, but not judgmental.”