Can there be a protagonist without an antagonist?

The protagonist is the hero or central character, the focus of the story and it's themes. So unless you define "antagonist" so broadly as to include all possible opposition such as bad luck, geography, and weather, stories are perfectly possible without one.

Consider "To Build a Fire" or "Hatchet" as stories with a protagonist lacking a proper opponent. Conversely, if you consider "antagonist" to indeed include any and all difficulties, then the statement "A Protagonist requires an Antagonist" is a tautology and your answer is no.