1.  1800 Census Index (online at GenealogyLibrary.com):•

1800

Chena, Edward, Jr.

VT

Rutland Co.

Brandon

00100-00100-00

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
1 male	16-25	1774-1784	= Edward (b. 1777)
1 female	16-25	1774-1784	= Elizabeth (b. 1779)

2.  1810 Census Index/Images (online at Ancestry.com; Image #1 of 6; extracted by Diana Gale Matthiesen):•

1810

VT

Rutland Co.

Brandon

Roll M252_65

p. 160/363

Ln. 15

Edward Cheney Jr

30010-10010-0-6-1-1-1-30-7-11

These data indicate:

No. & Sex	Age Class	Therefore Born	Individuals Inferred
3 males	9 or under	1800-1810	= Chapel (b. ca. 1809) = Hale (b. ca. 1804) = Gilbert (b. 1800)
1 male	26-44	1765-1784	= Edward (b. 1777)
1 female	9 or under	1800-1810	= Nancy (b. ca. 1807)
1 female	26-44	1765-1784	= Elizabeth (b. 1779)
0	Slaves/Blacks
6	Number of the Whole
1	Linnen Wheels
1	Spinning Wheels
1	Looms
30	Yards of Woolen Cloth
7	Yards of Linnen Cloth
11	Sheep

Listed one line below Richard GILBERT, six lines below Samuel CHENEY, and two lines above Daniel HARRINGTON.

3.  Scott Andrew Bartley, ed.  1997.  Vermont Families in 1791.  Vol. 1.  Genealogical Society of Vermont, Saint Albans, VT, pp. 87-88.  Gives a second daughter, Lois, as having been born ca. 1823.  Hardly likely as Edward Cheney died in 1812 and the first Lois survived (see next source), so one wouldn't expect a second daughter named Lois.  Or was "1823" simply a typo for "1813"? 

4.  Charles Henry Pope.  1897.  The Cheney Genealogy. (Self-published) Barta Press, Boston (online at GenealogyLibrary.com).  For excerpt on Edward Cheney, click here.