Is this quote, "If chance will have me king, why, chance may crown me/ Without my stir," an example of metaphor, simile, personification, or...

This quote is an example of personification.

Personification is a type of figurative language where something nonhuman is described as human or given human characteristics.  It is used to add emphasis or help the reader (or audience) appreciate an important thematic point.  In this case, the personification of chance emphasizes Macbeth’s ambition, but also his hesitancy.

When Macbeth gets a visit from three witches, they tell him that he is about to get a promotion. ...

This quote is an example of personification.

Personification is a type of figurative language where something nonhuman is described as human or given human characteristics.  It is used to add emphasis or help the reader (or audience) appreciate an important thematic point.  In this case, the personification of chance emphasizes Macbeth’s ambition, but also his hesitancy.

When Macbeth gets a visit from three witches, they tell him that he is about to get a promotion.  He will become Thane of Cawdor, and then king.  Macbeth is skeptical but excited about this development. 

MACBETH

Your children shall be kings.

BANQUO

You shall be king.

MACBETH

And thane of Cawdor too: went it not so?

BANQUO

To the selfsame tune and words. …  (Act 1, Scene 3)

Macbeth wants to be king, but as you can tell from your quote he doesn’t want to do anything himself to make that happen. Instead he personifies chance, and expects chance to do it for him.  In other words, if he just happens to be made king, without his having to do anything, that’s great!

When Macbeth finds out that Malcolm has been named King Duncan’s heir, he is annoyed.  He wanted to be king, and was just getting used to the idea.  The fact that he is promoted to Thane of Cawdor, having just killed the former man of that title in battle, inspires him. 

The Prince of Cumberland! that is a step
On which I must fall down, or else o'erleap,
For in my way it lies. Stars, hide your fires;
Let not light see my black and deep desires (Act 1, Scene 4)

Although this little aside is a big show, Macbeth doesn’t really have the follow-through to match his ambition.  The personification of chance emphasizes Macbeth’s inability to do anything himself.  His wife talks him into it, and plans everything out for him.  Otherwise he never would have been able to kill Duncan, and would have waited around for chance to make him king.