But strictly speaking; the chicken hatches from the egg. It's the hen that lay eggs. In Norwegian: Kyllingen klekker fra egget. Det er høna som legger egg.
Chicken in english is a general term for both hens and roosters, a hen is a chicken and a rooster is a chicken. Just like a woman is a human and a man is a human.
The chicken of course. How would she be able to love the egg if the egg came first? There would be no love....
Probably the egg. A long time ago some creature must've had a weird mutant baby that ended up being a chicken.
Technically, stative verbs like "love", "like", "want" etc. should not be used in continuous form, since they describe an ongoing state to begin with. However, this rule of thumb is becoming increasingly disregarded, so in the future "is loving" may possibly become standard.