The correct answer is - They wanted a word for their unique cultural identity.
The word chicano is a word used between the American that have Mexican origin (Mexican-Americans), with the purpose of representing their unique cultural identity. The word is mostly used as chicanos, for man and boys, though some women and girls too use it and adopt it, in the version of chicanas.
The Mexican-Americans have a unique culture. While they have the cultural basis in the Mexican, Latino culture, they are also Americanized to a certain degree, thus possessing traits of the English culture as well, making them unique in that department. In order to describe their culture, and themselves as part of it, they chose to use this word.