I stop obviously. There I sit with a dog and a chicken in my way, thus causing me to stop traffic.
So, I do what any person would do when they have something in front of their car. I honk my horn.
The dog was smart enough to take this signal to get out of the road. However, apparently my horn sounds somewhat like a chicken mating call or something, because this caused the chicken to further investigate. Thus it got right up to the front of my car, where I could no longer see it over the hood.
So there I sit. Presumably with a chicken somewhere near my front bumper, going, "What the fuck do I do now?"
If I cannot see the chicken, the people behind me certainly can't. Cars start honking. I hear one of the people going by in the left lane, tell the people that I have chicken in front of my car, so they stop honking.
Eventually someone from a nearby bus stop comes out and starts waving her coat at the chicken going "Shoo!" I can't see, but she tells me it won't move. Finally, she actually brings her coat in contact with the chicken, brushing it to the side of my car. I still cannot see said chicken. But the bus stop lady tells me it's safe to go, so I drive away.
As far as I know, no chickens were harmed in the posting of this message. (Although, eggs were involved with dinner, in the interest of full disclosure.)
And alas, I must report I was neglect in my duties, I never actually saw the chicken reach the other side.