One of the 33 miners trapped underground in San Jose mine outside Copiapo has become a father to a daughter named Esperanza, meaning 'hope' in Spanish.

Ariel Ticona may have a long wait before he gets to hold his first baby girl, but he will be able to see pictures of the birth via the capsules or "doves" which have become the miners' lifeline.

Baby Esperanza was born at a clinic in Copiapo, weighing 3.5kg.

Mother Elizabeth Segovia was planning to call her Carolina, but changed her plans in honour of "Camp Esperanza" or "Camp Hope" where relatives of the miners have been keeping an anxious vigil.

Segovia's mother, Maria Yanez, and grandmother to the new baby, said that while the birth was tinged with sadness, she knew it would lift her son's spirits.

"It's a little bit sad because my son was not present at the birth of his daughter. I would have liked him to be here, but he couldn't. He will see the video which will make him happier," she said.

One relative said mother and daughter were both in good shape.

Ticona and his 32 colleagues have been trapped nearly a mile underground since their mine shaft collapsed on August 5.

Their rescue, which involves drilling a new escape tunnel, is predicted to take months.