"Relates How Oliver Twist Was Very Near Getting a Place, Which Should Not Have Been a Sinecure."
Oliver’s punishment for asking for more is to be locked in a dark room for a week. Dickens suggests that Oliver is so depressed by his solitary confinement that the "gentleman in the white waistcoat" could have been proven right (i.e., that Oliver would be hanged) if Oliver had had a pocket-handkerchief with which to hang himself. Of course he doesn’t have one, because they’re considered a luxury item.
Then we skip scenes. Mr. Gamfield, a chimneysweeper, is coming down the road in front of the workhouse with his donkey, trying to figure out a way to pay his rent, and "alternately cudgelling his brains and his donkey" (3.3). We’d like to point out that this sentence uses an uncommon literary device: zeugma (pronounced "zoig-mah"). If you want to impress your teacher, just point this out. Using a verb to mean two different things in the same sentence ("cudgelling his brains and his donkey") is called zeugma. We love zeugma. It’s also very fun to say.
But back to Mr. Gamfield. He stops his donkey in front of the workhouse to read a notice posted on the gate, and the man with the white waistcoat (the one who thinks Oliver’s going to be hanged) is happy to see him look at it, because the notice is advertising that the workhouse has an unwanted orphan who will be given, along with five pounds, to anyone willing to sign him up as an apprentice.
Mr. Gamfield happens to need exactly five pounds to pay his rent, so he tells the gentleman in the white waistcoat that he needs an apprentice. Now, just to make this all very clear, here’s another Historical Context Lesson: young boys didn’t usually survive long as chimneysweeps. They had a bad habit of smothering in ashes, falling out of chimneys or off of roofs, or else being starved to death by their masters.
Back to the story: Mr. Limbkins, another of the parish officials, knows all this about chimneysweeps, so after a whispered conversation with the man in the white waistcoat, and other parish board members, they tell Mr. Gamfield that because Oliver is not likely to survive very long as a chimneysweep, Mr. G. can’t have the full five pounds.
They offer three pound ten, and after some debate, Mr. Gamfield agrees.
Mr. Bumble goes to release Oliver from his solitary confinement, and gives him extra gruel and even some bread. Oliver (understandably) assumes "that the board must have determined to kill him for some useful purpose, or they never would have begun to fatten him up in this way" (3.35).
Fortunately for Oliver, becoming someone’s apprentice required that some paperwork be signed by the local magistrate. And the magistrate, although oblivious to most things, can’t quite ignore the look of abject terror on Oliver’s face as he is about to sign the indentures.
So, Oliver is spared the fate of becoming a chimneysweep, and the notice advertising that an orphan is available as an apprentice is posted again on the workhouse gate.