Cantor Chocolate

Jill takes a bar of chocolate:

She removes the middle third and gives it to her sister, as shown:

This is what Jill has left now

She then removes the middle thirds from the two remaining chocolate bars and gives them to her sister again.

Jill's share of the chocolate this time

If she continues to do this indefinitely with each of the pieces she has left, will her sister eventually receive the entirety of the chocolate bar?