Chell has nearly no characteristics. We know she’s not one for talking. We know she’s female. We know at some point between Portal and Portal 2 she got a bit warm and pulled down the top part of her jumpsuit. We know nothing about her back story, other than speculation based on clues throughout the games (apparently one of the potato battery projects in Portal 2 has “By Chell” on it, and GLaDOS confirms that Chell is adopted in the “I literally do not have enough energy to lie” section), and the only thing we know for sure about her personality is that at some point she tested high for “tenacity.”
With such a non-characterized character, whose actions do nothing to influence the outcome of the storyline (the game can only end one way), can Chell be seen as anything other than the player’s avatar? If this is the case, then we should view all the elements in the game that are meant to psychologically affect Chell as being directed only at the gamer. All of GLaDOS and Wheatley’s taunts and praises are directed not at the person holding the portal gun, but at the person holding the Xbox controller.
At its core, Portal is a puzzle game. Rather than clicking on the bad guys to make them die, as with most first person shooters, the player has to utilize problem solving skills and do quite a bit of complex three-dimensional thinking. Moreso than other games, I feel that the Portal games rely on trial and error and the skills of the player. The plot is there, but the supposed protagonist could be replaced with just about anybody.
This is all just one way to look at the vagueness about Chell's character, but it's necessary to consider this possibility when attempting to interpret all the comments made throughout the games.