Which type of tree was the partridge sitting in, according to a well-known Christmas song?

That would be a Pear Tree.

The song is called "The Twelve Days of Christmas".

On the first day of Christmas

my true love sent to me:

A Partridge in a Pear Tree

On the second day of Christmas

my true love sent to me:

Two Turtle Doves

and a Partridge in a Pear Tree

On the third day of Christmas

my true love sent to me:

Three French Hens

Two Turtle Doves

and a Partridge in a Pear Tree

On the fourth day of Christmas

my true love sent to me:

Four Calling Birds

Three French Hens

Two Turtle Doves

and a Partridge in a Pear Tree

On the fifth day of Christmas

my true love sent to me:

Five Golden Rings

Four Calling Birds

Three French Hens

Two Turtle Doves

and a Partridge in a Pear Tree

On the sixth day of Christmas

my true love sent to me:

Six Geese a Laying

Five Golden Rings

Four Calling Birds

Three French Hens

Two Turtle Doves

and a Partridge in a Pear Tree

On the seventh day of Christmas

my true love sent to me:

Seven Swans a Swimming

Six Geese a Laying

Five Golden Rings

Four Calling Birds

Three French Hens

Two Turtle Doves

and a Partridge in a Pear Tree

On the eighth day of Christmas

my true love sent to me:

Eight Maids a Milking

Seven Swans a Swimming

Six Geese a Laying

Five Golden Rings

Four Calling Birds

Three French Hens

Two Turtle Doves

and a Partridge in a Pear Tree

On the ninth day of Christmas

my true love sent to me:

Nine Ladies Dancing

Eight Maids a Milking

Seven Swans a Swimming

Six Geese a Laying

Five Golden Rings

Four Calling Birds

Three French Hens

Two Turtle Doves

and a Partridge in a Pear Tree

On the tenth day of Christmas

my true love sent to me:

Ten Lords a Leaping

Nine Ladies Dancing

Eight Maids a Milking

Seven Swans a Swimming

Six Geese a Laying

Five Golden Rings

Four Calling Birds

Three French Hens

Two Turtle Doves

and a Partridge in a Pear Tree

On the eleventh day of Christmas

my true love sent to me:

Eleven Pipers Piping

Ten Lords a Leaping

Nine Ladies Dancing

Eight Maids a Milking

Seven Swans a Swimming

Six Geese a Laying

Five Golden Rings

Four Calling Birds

Three French Hens

Two Turtle Doves

and a Partridge in a Pear Tree

On the twelfth day of Christmas

my true love sent to me:

12 Drummers Drumming

Eleven Pipers Piping

Ten Lords a Leaping

Nine Ladies Dancing

Eight Maids a Milking

Seven Swans a Swimming

Six Geese a Laying

Five Golden Rings

Four Calling Birds

Three French Hens

Two Turtle Doves

and a Partridge in a Pear Tree

It was in a pear tree.