I haven't eaten an apple ...... a long while.

I haven't eaten an apple for a long while.
In this context, "for" is the correct preposition to use to indicate the duration of time during which the action of not eating an apple has occurred. "For" is commonly used with expressions of time to specify the duration of an action or event. Therefore, "for" is the correct choice to complete the sentence, accurately conveying the duration of time during which the speaker has not eaten an apple.