Individual Details

One record says she is the daughter of Richard, and that she is a twin. However, the birth record for Elizabeth a twin born on this date that is given in the above record is the daughter of Samuel and Elizabeth born in Chelmsford. This is the source: A Genealogy of Several Branches of the Whittemore Family, p. 51; it specifies that Elizabeth has a birthdate 29 May 1699.
Here is the birth record for that date for Elizabeth Chamberlain.
BIRTH : 1699 LOCATION : Chelmsford, Middlesex, Massachusetts, United States VOLUME : Chelmsford - V1 PAGE : 42 TEXT : Elisabeth, d. twin, Sam[ue]ll and Elisabeth, May 29, 1699.

Here is the marriage record for Samuel Chamberlin and Elizabeth Emerson
MARRIAGE : 1685 LOCATION : Chelmsford, Middlesex, Massachusetts, United States VOLUME : Volume 1 PAGE : 293 TEXT : CHAMBERLIN, Samuel (1645-1722) & Elizabeth [EMERSON?] (?1660-1722); by 1685; Chelmsford

But Elizabeth Chamberlain is described as "of Boston" in her marriage record.
And Daniel Whittemore married Mary Chamberlane of Boston 22 Jan 1719. Daniel Whittemore is the brother of Joseph and Mary is the twin of Elizabeth who was born to Samuel and Elizabeth.

Yet another source says daughter of John and Hannah Chamberlain -- NEHGR, January 1953, p. 32, Vol CVII

Birth	29 May 1699	Chelmsford, Middlesex, Massachusetts
Marriage	6 Feb 1717/18	Boston, Suffolk, Province of Massachusetts - Joseph Whittemore
Death	1721

Spouse	Joseph Whittemore (1693 - 1735)
Child	Edmund Whittemore (1718 - 1786)

Father	Samuel Chamberlain (1645 - 1721)
Mother	Elizabeth Emerson (1660 - 1722)
Sibling	Samuel Chamberlain (1685 - 1769)
Sibling	Joseph Chamberlain (1687 - )
Sibling	Elizabeth Chamberlain (1694 - 1694)
Sibling	Benjamin Chamberlain (1694 - )
Sibling	Mary Chamberlain (1699 - )

Notes