Take the fox over, return with nothing. Go over with one chicken, return with the fox. Go over with the second chicken, return with nothing. Finally, take the fox over.

Or let:
Man = M
Fox = F
Chicken1 = C1
Chicken2 = C2

This is how they cross the river:

1. M,F →
2. ← M
3. M,C1 →
4. ← M,F
5. M,C2 →
6. ← M
7. M,F →