Born on September 29, 1691, he was raised a Presbyterian until after his father died when his mother became a servant in a Catholic household. Then he was raised Catholic and was baptized when he was thirteen. He entered the English College in Douai in 1705 and remained there until he returned to England in 1730. Challoner was ordained a priest in 1716 and served as an adminstrator at Douai for many years until becoming a missionary priest in London among the poor; although the recusancy laws were not as strictly enforced at that time, Father Challoner was still disguised as a layman and was careful not to attract official attention the the Masses and other Sacraments he celebrated in all kinds of locations.
In 1728 he had published his first work, Think Well on It. William Hyland discusses his many other published works in this Touchstone article.
Among his works, including a revision of the Douai-Rheims Bible and several devotional books, I think his most interesting were the historical and hagiographical efforts--books on the Anglo-Saxon and Medieval saints and especially on the Catholics martyrs who suffered in England from the reign of Henry VIII to that of Charles II. Those works provided the tiny minority of Catholics in England a vision of their past and indeed of its glories. In their own age they were nearly forgotten and quite ignored--not even worth persecuting!
Strangely enough, that latter condition changed after Parliament passed the Catholic Relief Act of 1778. Lord Gordon, President of the Protestant Assocation enraged the mobs so in 1780 that various No Popery riots took place (as recounted in Charles Dickens' Barnaby Rudge), as well as a march on Parliament, leading to many arrests and executions. The mobs also attacked the Embassy buildings of Bavaria and Sardinia, as well as the homes of wealthy noble Catholics. Bishop Challoner, aged 89, had to hide--just like a 16th century priest of old--until the mobs left his London home. The shock and terror of that near escape was too much for him. Bishop Challoner suffered paralysis two days before his death.
He was succeeded as Vicar Apostolic by his Coadjutor James Talbot; the last to hold that title was Nicholas Wiseman, who became the first Archbishop of Westminster in 1850.