Chava is the third to go—and boy, does she go. She ups the stakes—really, she pulls up the stakes entirely—by rejecting her family and culture to marry a non-Jewish man named Chvedka.
When we meet Chvedka, he's just some local goy who is always hanging around Tevye's house for some reason. Some reason named Chava.
Like all of Tevye's children (expect maybe Shprintze), Chava has a mind of her own. Check out the way she talks back to Tevye when he's trying to convince her not to marry Chava:
"Is it a fault in your eyes," [Chava] said, "that a person works with his hands? Don't you yourself work? And don't we work?"
"Yes, yes, you're right. We have a special verse in the Bible: For thou shall eat the labor of thy hands—if you don't work, you won't eat. But still and all […] you mustn't forget whence you come and whither you go—who you are and who he is."
"God created all people equal," she said to me.
"Why should the world be like that? […] Why did He create it like that? […] That's why God gave us reason, so we could ask questions." (6.23-33)
Chava goes right up against Tevye, matching each of his Biblical quotations with one of her own. (See what happens when you let women get education? Next thing you know, they're talking back and refusing to shave their legs.)
We have to say, Chava seems pretty cool. It's one thing to marry the local tailor; it's another to follow your heart to such an extent that your father decides to declare you dead. Not that we're recommending that, or anything. Just saying.
Because, really, the whole thing is pretty heart-wrenching. Poor girl runs away from home, hides out at the house of the priest, and then has to listen to her dad in the next room begging the priest to return her. And then, when she sees her dad in the street and chases after him, he refuses to even acknowledge her existence.
Even the story doesn't acknowledge her existence. One thing to notice is that, unlike Tzeitl and Hodl, we never get Chava's take on the whole experience. Her sisters get to make little speeches about the awesomeness of their love, but Chava disappears from the story just like she disappears from her family's life.
The point of all of this? In order to become part of the majority culture around her, Chava has to completely bury her original identity. For Tevye, and it seems like for Sholem Aleichem, this is a horrible betrayal. The majority culture Chava is rushing off to join thinks nothing of killing, scapegoating, and generally tormenting its Jewish neighbors. Chava's total loss of her family is a result of her decision, and though we pity her, we're really not supposed to sympathize.
We know we're not really supposed to sympathize, because we've already seen Tevye be pretty cool about his girls marrying for love. So by the time we get to this story, we know that he's not rejecting Chava because she chooses her own husband but because by marrying a Gentile, she's choosing to side with her people's oppressors.
Check out Tevye's explanation: "the pain is great, but the shame, the shame is even greater!" (6.3). To Tevye, the shame of having a child reject her culture is worse than the pain of losing her. And this is also why it makes sense that as soon as Chava leaves behind her non-Jewish life, Tevye reconciles with her.