"My dog eats chicken."
Translation:Il mio cane mangia pollo.
Basically, il mie does not exist in Italian. It is Il mio pollo, La mia cena, I miei Cavalli (do not confuse the capital letter i with the English equivelant) and Le mie cane. These are the four main ways to indicate and describe that an object or thing belongs to you in Italian.
Sidenote Sorry for reacting to this but I feel (as a language teacher myself) that Ellieb09's explanation was a little bit to technical and know from both science and experience that using metalanguage to explain language does not help people unless they have a profound knowledge of metalanguage first.
Let's say in 70% of the cases you must use it, and in 90% you can.
The good rule is to learn where NOT to put it.
"Mia madre" "Mio padre" and other family members. Like "Lo ho detto a mia madre."
(Notice that "la mia matrigna" is not considered a family member, and not even "il mio padrino")