"I do not want this chicken."
Translation:Я не хочу эту курицу.
The direct object of a transitive verb uses the accusative case. Because "this chicken" is the direct object of "I dont want" ета курица becomes ету курицу.
No it can't be. After the verb хотеть fellows the accusative case. And the accusative case changes the ending of female nouns from -a to -y. For more info see http://www.russianlessons.net/grammar/nouns_accusative.php
"не хочу эту курицу" was counted wrong. I thought you can drop the pronouns я,ты, etc because the conjugation implied them?
I can't think of a definite rule when you should drop the pronouns and when not. It depends on the context. Here, the basic translation is with the pronoun, you'd better remember it as the default.
Unlike Spanish, it is not common to drop almost all personal pronouns in Russian.
Is it grammatically wrong to drop it here? Does it change the meaning? I'm fine doing it in the future, but I want to make sure I understand why too :)
It is not grammatically wrong, but just less common. Like, a child is being stubborn and does not want to eat chicken his mother urges him to eat. Не хочу эту курицу!
Side question: If you DID want chicken, is it still эту курицу, or is it эта курица?
It is still эту курицу, because it remains the direct object. Я хочу эту курицу.
Нет means "no" Не means roughly "not" or "do not". So Я не хочу means I do not want. Я нет хочу would be like I no want. It might get your point across but people would look at you funny.
Why it is not "этой курицы"? Doesn't a negated transitive verb wants the object in genitive case?