The tale is set in a forest and begins with "once upon a time". Timmy Tiptoes is "a little fat comfortable grey squirrel" living in a nest thatched with leaves in the top of a tall tree with his little wife, Goody. Over the course of several days, the two collect nuts in their little sacks for the coming winter and spring, and store the nuts in hollow tree stumps near their home. Timmy wears a red jacket he removes while working, and his wife wears a pink dress and apron. When the stumps are full, the couple make use of a tree-hole that once belonged to a woodpecker. The nuts rattle "down – down – down inside", and Goody wonders how they will ever retrieve them. Timmy reminds her he will be much thinner by springtime and will be able to pass through the little hole.
In an aside, the narrator tells the reader that the couple had great quantities of nuts because they never lost them, noting that most squirrels lose half their nuts because they cannot remember where they buried them. Silvertail is the most forgetful of squirrels in the wood, and, while trying to find his nuts, digs up another squirrel's hoard. A commotion erupts among the nutting squirrels, and, as ill luck would have it, a flock of birds fly by singing "Who's bin  [sic] digging-up my nuts?" and "Little bit-a-bread and-no-cheese!" One bird finds a perch in the bush where Timmy is working and continues to sing about digging up nuts. The other squirrels take notice, suspect Timmy of robbing others of their hoards, rush upon him, scratch and cuff him, chase him up a tree, and stuff him with great difficulty through the woodpecker's hole. Silvertail suggests they leave him there until he confesses.
Timmy lays "stunned and still" on the peck of nuts he has stored in the hollow tree while Goody searches fruitlessly for him. Eventually, Timmy stirs and discovers himself in a mossy little bed surrounded by ample provisions. Chippy Hackee, a small striped chipmunk, tends him with kindness, mentioning that it has been raining nuts through the top of tree and he has also "found a few buried". The chipmunk coaxes Timmy to eat the nuts and Timmy grows "fatter and fatter!"
Goody is very concerned about her husband's disappearance, but has gone back to work collecting nuts and hiding them under a tree root. Mrs. Hackee, Chippy's wife, emerges from beneath the root to demand an explanation regarding the shower of nuts into her home. Eventually, the two ladies complain about their runaway husbands, but the chipmunk knows where her husband is camping-out because a little bird has told her. Together, they hurry to the woodpecker's hole and hear their husbands deep within the tree singing:
"My little old man and I fell out,
How shall we bring this matter about?
Bring it about as well as you can,
And get you gone, you little old man!"
Mrs. Hackee refuses to enter the tree because her husband bites, but Goody calls to her husband and he comes to the hole with a kiss for her. He is too fat to squeeze through the hole, but Chippy Hackee (who is not too fat) refuses to leave and remains below chuckling. A fortnight later, a big wind blows off the top of the tree, and Timmy makes his escape. He hurries home through the rain, huddling under an umbrella with his wife.
Chippy Hackee continues to camp-out in the tree stump for another week, but a bear comes lumbering through the neighbourhood (looking for nuts perhaps?) and Chippy decides it's time to hurry home. He suffers a cold in his head and is quite uncomfortable. Timmy now keeps the family nuts "fastened up with a little padlock", and Goody is seen in the accompanying illustration sitting outside the nest tending three tiny babies. "And whenever that little bird sees the Chipmunks, he sings – 'Who's-been-digging-up my-nuts? Who's been digging-up my-nuts?' But nobody ever answers!" Chippy Hackee and his wife are seen in the last illustration trying to drive the little bird away with their tree-leaf umbrella.
Potter's idea to make the squirrel grow so fat he cannot escape the tree was imitated by A. A. Milne in Winnie the Pooh.

Question: Why does Timmy keep getting fatter while in the tree?
Answer: Chippy keeps encouraging him to eat more nuts.
Alternative answer: By eating the nuts.