"There was an old woman lived under a hill" is a nursery rhyme

Nursery rhyme

The term nursery rhyme is used for "traditional" poems for young children in Britain and many other countries, but usage only dates from the 19th century and in North America the older ‘Mother Goose Rhymes’ is still often used.-Lullabies:...

 which dates back to at least its first known printing in 1714. It has a Roud Folk Song Index

Roud Folk Song Index

The Roud Folk Song Index is a database of 300,000 references to over 21,600 songs that have been collected from oral tradition in the English language from all over the world...

 number of 797.

Text

There was an old woman lived under the hill,

And if she's not gone she lives there still.

Baked apples she sold, and cranberry pies,

And she's the old woman that never told lies.

Origins and Development

In 1714 these lines:

There was an old woman

Liv'd under a hill,

And if she ben't gone,

She lives there still--

appeared as part of a catch in The Academy of Complements. In 1744 these lines appeared by themselves (in a slightly different form) in Tommy Thumb's Pretty Song Book

Tommy Thumb's Pretty Song Book

Tommy Thumb's Pretty Song Book is the earliest extant printed collection of English language nursery rhymes, published in London in 1744. It was a sequel to the lost Tommy Thumb's Song Book and contains the oldest version of many well-known and popular rhymes, as well as several that have been...

, the first extant collection of nursery rhymes. One eighteenth-century editor, possibly Oliver Goldsmith

Oliver Goldsmith

Oliver Goldsmith was an Irish writer, poet and physician known for his novel The Vicar of Wakefield , his pastoral poem The Deserted Village , and his plays The Good-Natur'd Man and She Stoops to Conquer...

, added a note: "This is a self evident Proposition which is the very Essence of Truth. 'She lived under the hill, and if she is not gone she lives there still', Nobody will presume to contradict this."

The 1810 edition of Gammer Gurton's Garland included a variant

Pillycock, Pillycock, sate on a hill,

If he's not gone--he sits there still.

Edgar, in Shakespeare's King Lear

King Lear

King Lear is a tragedy by William Shakespeare. The title character descends into madness after foolishly disposing of his estate between two of his three daughters based on their flattery, bringing tragic consequences for all. The play is based on the legend of Leir of Britain, a mythological...

, appears to refer to this version when he says "Pillycock sat on Pillycock hill," which indicates that the rhyme was known as early as the first decade of the seventeenth century. The final lines first appeared in print c. 1843.