This phrase is the name of the first chapter in Oliver Twist. Let's take a look at a few other chapter names:
Source: Dickens, C. (1838). Oliver Twist.London, England; Bentley's Miscellany. http://etc.usf.edu/lit2go/50/oliver-twist/
Chapter 1: Treats of the Place Where Oliver Twist was Born and of the Circumstances Attending His Birth.
Chapter 2: Treats of Oliver Twist's Growth, Education, and Board.
Chapter 3: Relates How Oliver Twist was Very Near Getting a Place Which Would Not Have Been a Sinecure.
Chapter 11: Treats of Mr. Fang the Police Magistrate; And Furnishes a Slight Specimen of His Mode of Administering Justice.
Chapter 24: Treats on a Very Poor Subject. But is a Short One, and May be Found of Importance in this History.
Chapter 34: Contains Some Introductory Particulars Relative to a Young Gentleman Who Now Arrives Upon the Scene; And a New Adventure Which Happened to Oliver.
The examples I gave, and a few others, have chapter names that follow the pattern "Chapter XX does Y." Chapter 11, in particular has this structure twice.
So it looks like treats is being employed as a verb.
As for meaning? Treats can mean something like "provides." In modern English, it is usually used for desirable things and is usually followed by "to." (e.g. I treated the basketball team to ice cream after the game) I don't know if the convention wasn't established when Dickens wrote these chapter headings, or if he is just being colorful, but it looks like your quote means:
Chapter One describes the place where Oliver Twist was born.
Also, with acknowledgement to a comment by @Bob Jarvis: Dictionary.com's 9th definition for treat gives an example that uses treats + of: "to deal with a subject in speech or writing; discourse: (example) a work that treats of the caste system in India."