I think you can and my colleage thinks you cannot!
You can't even declare private virtual methods. The only time it would make any sense at all would be if you had:
public class Outer
{
private virtual void Foo() {}
public class Nested : Outer
{
private override void Foo() {}
}
}
... that's the only scenario in which a type has access to its parent's private members. However, this is still prohibited:
Test.cs(7,31): error CS0621: 'Outer.Nested.Foo()': virtual or abstract members cannot be private
Test.cs(3,26): error CS0621: 'Outer.Foo()': virtual or abstract members cannot be private