I think that as Cave Johnson and Caroline were close and worked together, Chell could have been the daughter of the two, however was adopted by Doug Rattman as the two did not want Chell to become an obstacle in the workplace.
I think this as GLaDOS makes fun of Chell throughout the story, saying that she is adopted, and this links to the above. It also makes sense as in Portal 2: Lab Rat Doug follows Chell throughout the entire facility, which ties in as he might want to protect her. Chell might not talk as Cave Johnson, her supposed dad, dies in the events before the GLaDOS takeover.
And another thing finally, the thing I forgot to mention about the story is the other meaning to the ending. In Greek Mythology, heaven is a cornfield. When you die, you hear singing and you're accompanied by your best friend (the Companion Cube). The turrets shot her, and she heard singing. GLaDOS may not of spared her after all.
What do you think? Comment saying what!
And to anyone who says "YOUR TAKIN THIS WAY TO FAR!", I love Portal and know near enough everything about the Half Life/ Portal series.