"A bear is chasing us!"
Translation:Honí nás medvěd!
If this sentence wouldn't an exclamation, than it would be correct. Sentence "Medvěd honí nás." emphasizes word nás. (that it is us who is chased).
It is very strange.
"Ten medvěd honí nás!" is possible for "The bear is chasing US!" when you say he is chasing US and not something else, but for "a bear" it is really strange.