Why did the chicken cross the road?

Because it's afraid of the car (or anything that's making a noise or seems threatening).

I have seen this many times, because we've had chickens. Chickens will cross the road for two reasons: They either want to cross because they have some urge to cross, such as to look for food on the other side. Or they hear a car coming, get startled, and start running towards their own flock, which might be on the other side. They feel safer with the other chickens and are willing to risk crossing the road to be with their own group. Safety in numbers overrides the risks of crossing the road. I think the question of why did the chicken cross the road came about because it happens so frequently that a chicken will cross the road right in front of your car and you wonder why it would do that (squirrels and deer do it too).

Which came first, the chicken or the egg?

The egg came first, obviously.

f you have an egg in front of you, that egg came after its chicken mother. If you're looking at the chicken, it came after its egg. 

Zoom out and you get:

Before there were chickens many animals laid eggs. Later on after millions of years of evolution, chickens laid eggs. So, the egg came before the chicken.