Mary Cheney, the vice president's lesbian daughter, had her first child this morning at Sibley Hospital in Washington, D.C.
Samuel David Cheney was born at 9:46 a.m., weighing 8 lbs., 6 oz.
His parents are Mary and her partner, Heather Poe.
"The vice president is pleased to be a grandfather for the sixth time," spokeswoman Megan McGinn said.
The vice president's office announced in December that Mary was expecting her first child and a spokeswoman said at the time that he and his wife were "looking forward with eager anticipation to the arrival of their sixth grandchild."
Cheney bristled when the subject came up in a notably testy exchange in January with CNN's Wolf Blitzer.
Blitzer asked the vice president about a statement from Focus on the Family about whether having a child outside of a married mother or father is best for the child.
Cheney said Blitzer was "out of line" even asking the question about Mary Cheney and said he fundamentally disagreed with Blitzer's perspective.
But Blitzer did not really offer his perspective and the only question he asked was whether Cheney wanted to respond to the Focus on the Family statement.
Blitzer said it was a question that has come up and it's a "responsible, fair question."
Vice President Cheney said then that he was delighted to have a sixth grandchild and thinks the world of both of his daughters and all of his grandchildren.
His daughter, Elizabeth, has five children with her husband Philip Perry: three daughters, Kate, Elizabeth and Grace and two sons, Philip and Richard.
President Bush told People magazine in December that Mary Cheney would be "a loving soul to her child."
The president said this in response to a question about his comment from 2005 that "a child is raised in a married family with a man and a woman."
"The vice president took me aside and gave me the good news. He and his wife, Lynne, are very happy for Mary," Bush said. "I think Mary is going to be a loving soul to her child. And I'm happy for her," Bush said.
ABC News' Ann Compton asked the president in December if, in light of Mary's pregnancy, there were any changes in the law that he would support that would give same-sex couples greater access to legal rights, hospital visits, insurance.
The president said he thinks the government should review the law "to make sure that people are treated fairly."
But he punted on Mary Cheney specifically, saying it was a "personal matter" for Vice President Cheney and his family.
"I know Mary. And I like her. I know she's going to be a fine, loving mother," Bush said.