encounter between polar opposites with their dogs

Hard to say, as opposites by their nature must be similar enough to compare. A chicken is so complex, that you would have to pick a factor to oppose. A cow is large and slow, a chicken is small and fast. They could be opposite.

A fish breathes water, a chicken breathes air. Opposite.

Chickens hate to swim, ducks love it. Opposite.

If you meant an animal completely different from a chicken in every way, they would likely be too different to consider an opposite. Perhaps a tardigrade or a giant cave spider.