What is the simile that Hawthorne uses to describe the emotions on the face of the stranger as he spots Hester in Chapter 3 of The Scarlet Letter?

Actually, there are two pertinent similes here.  A simile, of course, is a form of figurative language that makes a comparison using the words "like" or "as."  There is one simile when Chillingworth first spots Hester; however, there is a different one when he recognizes Hester.  Here is the first:

At his arrival in the market place, and some time before she saw him, the stranger had bent his eyes on Hester Prynne.  it was carelessly, at first, like a man chiefly accustomed to look inward, and to whom external matters are of little value and import unless they bear relation to something within his mind. (Hawthorne 67).

This is an interesting simile indeed because before we are even introduced to the true evil of Hester's husband, we learn that he has little compassion for anyone in any horrible situation (such as a nameless woman being ridiculed on a scaffold) unless that person somehow pertains to him.  In my opinion, when he describes Chillingworth "like a man chiefly accustomed to look inward," Hawthorne describes Chillingworth as totally and absolutely selfish.

Here is the second simile (found immediately after the first):

Very soon, however, his look became keen and penetrative.  A writhing horror twisted itself across his features, like a snake gliding swiftly over them, and making one little pause, with all its wreathed intervolutions in open sight. (67)

Ah, here the true evil nature of Chillingworth is revealed.  What better symbol to use within this simile than the symbol of the snake (the most common symbol of evil).  What a disgusting image!  He recognizes his wife and his features twist in a snakelike horror.  This is a character meant to be despised from the start!  Heck, just look at his name!