Does the following collection represent a Gregorian chant mode, or is it a scale?
This is the C-Dorian scale. We know this because Dorian lowers the third and seventh of the major scale, so from C major:
C D E F G A B
we just lower the third and seventh (E and B) to get the collection you posted.
(Dorian is also the natural minor scale with a raised sixth, if you want to go that route. You'll get the same result.)
As for whether or not it's a mode or a scale: in this case, it's kind of both. (It's a bit like how a square is a rectangle, but not all rectangles are squares.) This is a scale of the C-Dorian mode.
With such little context, I think it's better to ask "What collection is this?" instead of "Is this a mode or a scale?"
Edit: Just to add some further clarification, a mode is often understood as a rotation of a scale. So if we take the B♭-major scale:
B♭ C D E♭ F G A B♭
we can "rotate" it to begin on different members of that scale. If you rotate to start on C, you get:
C D E♭ F G A B♭ C
the exact same C Dorian from your question.
Another way of looking at this is that all of the notes belong in a major scale and key. The key of Bb major. When a set of notes starts and centres on the second note of the major scale, it's known as Dorian mode. And because this set starts on C, it's C Dorian. Please note - it's not known as Bb Dorian - for reasons Richard has noted.
It's a scale in the Dorian mode transposed down a whole step (C → B♭).