YOU SAID:

I have a rooster that wakes up early

INTO JAPANESE

早く目を覚ます鶏がいる

BACK INTO ENGLISH

I have a chicken awake early

INTO JAPANESE

私は早起きの鶏を持っている

BACK INTO ENGLISH

I have an early rising chicken

INTO JAPANESE

私は早起きチキンがあります

BACK INTO ENGLISH

I have an early riser chicken

INTO JAPANESE

私は早起きチキンを持っています

BACK INTO ENGLISH

I have an early riser chicken