Son of the doctor Marin Cureau de la Chambre and brother of François Cureau de La Chambre, he was struck down with deafness and had to abandon his medical studies.
He travelled to Italy and became friends with the sculptor Gian Lorenzo Bernini and the art historian Carlo Cesare Malvasia.
He studied theology and in 1664 he published a collection of his father's works and attended the salon of the marquise de Sablé.
He died in the famine of 1693, during which he ran out of food trying to help the poorest of his parishioners.
La Chambre had a scholarly reputation and corresponded with Pierre de Fermat, but the only written works he left were panegyrics and funerary orations for Theresa of Avila, Bernini, Maria Theresa of Spain, Pierre Séguier, Rose de Sainte-Marie de Lima, Charles Borromeo and Saint Louis.