Chavaleh

Chagall's the Promenade

Chavaleh (Chava+-leh) is the diminutive form of Chava. Essentially, like calling your daughter Katherine "Katie", likely after she's grown out of enjoying being called Katie. Calling her "little Chavaleh" is extra diminutive, and has extra emphasis for his reminiscing about her being a child.
He also calls her "Little bird" which in Yiddish would be Feygeleh, which rhymes with Chavaleh, though "little bird" does not. In dated usage feygeleh is a little bird or a very young girl (more modern usage is a male homosexual and is very much an insult).

This is one of the most tragic scenes, as, when Chava attempts to get Tevye to understand her choice (to marry the non-Jewish Fyedka), Tevye utterly rejects her. The next morning we learn Chava has eloped, and a priest has married her and Fyedka.
After learning Chava has eloped instead of accepting Tevye's rejection of Fyedka, Tevye declares her dead. This is not at all surprising with a historical lense on interfaith marriage in Jewish culture at the time. Below are some resources about Interfaith marriage in Jewish culture.
- On the left is a link to an article about intermarriage for American Jews, which includes brief information on cutting out children who intermarry, to the point of sitting Shiva (a mourning custom) as if they had truly died.
- The middle video is a brief Interview investigating interfaith marriage in the Early 20th Century
- The right link is to a long article on marriage, which the relevant statement is this: "Intermarriage rates remained extremely low [after WWI] in Poland and Lithuania while they rose in urban centers in the Soviet Union." From this we can extrapolate that Pre-WWI, which is the time Fiddler on the Roof is set, intermarriage rates for Jewish people were extremely low.