Actually, this is possible using a small trick. After you define your choices, set the first choice to be something like "Select a value". Then, go to Advanced settings tab, at the bottom select ValidatorDefiniton. Set the RegularExpression, for instance:
This will match all values starting with the entered string - the default value entered. This will force the user to select different value, making the dropdown list as if it is required. The error message shown will be the text in the RegularExpressionViolationMessage field.
This is the easiest way to achieve the 'required' dropdown, which I can think of, without custom development.
However, you should change your regular expression if you have set one, to match the not selected value as well, which is a drawback.
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