Most of the Biographical Dictionaries and Encyclopedias are agreed that he was born on 2^nd January 1647 at Friston Hall in Suffolk to Thomas Bacon Esquire and Elizabeth (nee Brooke) Bacon, but I have not been able to find a baptism register entry for Nathaniel. The Suffolk parish registers are not online yet, although Ancestry is currently digitising and indexing them, so hopefully once that project is complete I will be able to confirm this.

Hugh Chamberlen, styled the elder to avoid confusion with his son, also called Hugh, was born about 1634. According to Wikipedia, he was born in the parish of St Anne's Blackfriars between 1630 and 1634, but no baptism record has been found.

Hugh Chamberlen the younger was born on 16^th March 1663 and baptised 30^th March 1664 at St Christopher le Stock in the City of London. The church which no longer exists was on Threadneedle Street. It was damaged in the Great Fire of London which happened 2 years after Hugh's baptism.