The Tolkien novel beginning “In a hole in the ground there lived a hobbit” is The Hobbit.
The Hobbit, or There and Back Again, was published by George Allen & Unwin on 21 September 1937. Its opening sentence introduces Bilbo Baggins, a comfort-loving hobbit whose quiet life changes when Gandalf and a company of dwarves arrive at his home. Bilbo eventually joins their journey toward the Lonely Mountain.
The novel was written before The Lord of the Rings and has a lighter, more directly fairy-tale-like tone. Its plot includes the encounter with Gollum and the discovery of the One Ring, although the significance of that ring changed as Tolkien developed the later mythology.
Readers sometimes attribute the opening to The Lord of the Rings because Bilbo and the ring are central to both works. The sentence, however, belongs specifically to The Hobbit. The book’s subtitle, There and Back Again, also appears in-universe as the title of Bilbo’s memoir.