A Rooster is a high-level monster (around 80) that is very similar to a chicken, and indeed they are found together.
Specifically, players can find at least one in Tenzing's yard on Death Plateau. There is also a rooster in the chicken pen in Rellekka and in miscellania market.
The attackable ones are Free to play, but there is a rooster in the farm near Falador standing on the top of the box in the chicken pen even on a Members world. It looks exactly like the Good Chicken, a former random event and a boss monster in the questRecipe for Disaster. However, that one cannot be attacked. Roosters give 500 experience in Slayer per kill.