The Unreliable Detective

The detective is lying to us. Not incompetent, not confused - deliberately, carefully lying. We should be able to feel it without being certain. Write an opening chapter that introduces a detective figure investigating something (crime, disappearance, mystery of any kind) in which the narrator's account contains at least one visible crack - a moment where their version doesn't quite hold. The crack should be subtle. We should only notice on the second read.