Oliver is a mean-spirited old man who's beginning to suffer the symptoms of Alzheimer's. He has spent his life pushing people away, and now that he needs help, he's reluctant to ask for it. Convinced that his landlord and his daughter are plotting to take his money, Oliver collects all of his savings one morning and sets out for the bank.
As he wanders lost through the streets of downtown Los Angeles, he encounters Raymond, an out-of-work actor who's just been kicked out by his boyfriend and who's searching for something real in a world that, for him, has lost all substance. Raymond encounters the old man roaming around lost, picks him up, and attempts to help him find his way home. Also in search of Oliver is his daughter, Midge. Although she's been estranged from her father for years, she adopts Oliver's cause as a way of coping with her own loneliness and lack of focus in life.
As Oliver and Raymond circle the streets, Oliver makes a startling claim. He boasts that he's murdered his landlord. Not the kind of real experience Raymond was seeking, but something that powerfully engages his imagination. When Raymond finally drops Oliver at his apartment and finds that Oliver has left all of his money behind in Raymond's car, his involvement in the old man's life deepens.
Both Raymond and Midge spend the next several days in a cat-and-mouse game with Oliver—Raymond trying to balance his guilt about keeping Oliver's money with his desire to understand the old man's predicament, and Midge trying to find a way to be a dutiful daughter while protecting herself from the emotional pain that Oliver relentlessly inflicts upon her. While their conflicting agendas attempt to both help and take advantage of Oliver, both characters unwittingly further the old man's delusions.
An Awfully Good Alibi is a three-character tragedy of errors. Midge and Raymond desperately seek to carve out identities for themselves, as Oliver slowly loses his. What the three share is stubborn pride. Ultimately, pride is what Raymond and Midge must defeat in order to escape the kind of lonely end that Oliver inevitably faces.