Puzzle 005: River Crossing

ナゾ００５　川を渡そう
犬１匹、猫２匹、ヒヨコ３羽を
いかだに乗せて向こう岸へ渡りたい。
いかだに乗せられるのは自分以外に
２匹までだ。ただし人がいない場所で
猫と犬が同じ数になると、犬が猫を
追い回し、ヒヨコが猫と同じ数か
少ない数になると猫がヒヨコを追い
回すので、それは避けない。
向こう岸に動物達は集合できるかな？

Translation
You need to take one dog, two cats and three chicks across the river. You can only take two animals with yourself at any time. You cannot leave the dog and cats together on their own, as the dog will chase the cats; you cannot leave the chicks and cats together on their own as the cats will chase the chicks (it is in their nature.)
Can you cross the river with all of your animals?

Notes on Puzzle
A standard river crossing puzzle. The logic for these doesn't change much.
The shortest number of moves you need to transport the animals is 7.