Language plays an important role in the constitution of subjects, since it is the means by which we appropriate the culture around us, build up our understanding of the micro- and macro- universe, and establish our social and affective relationships. However, despite its unquestionable importance for human beings, the possibility of its development in deaf people has been denied over the centuries, as they have been deprived of the opportunity to learn Sign Language. The origins of this opposition to Libras (Brazilian Sign Language), which can be found in the majority in deaf children’s families as well as in schools, arises from myths and prejudices perpetuated in relation to deaf people and their natural language, are investigated, as a means to overcoming it. The primary objective of this paper, which arises from this discussion, is to show the importance of giving deaf children the opportunity to learn this language from an early age, for their full development. For this purpose, some studies are indicated that have been carried out with deaf children of deaf parents who have been able to acquire Sign Language as their fi rst language, in their earliest contacts with their surroundings. These studies conclusively show the importance of this early exposure to sign language, as it enables these children to build up a comprehensive and authentic language, reaching the same levels of development as hearing children who grow up in an oral-auditive linguistic environment.