There is strong empirical evidence on the universal development of phonological awareness from large to small units. However, comparatively little research has been conducted to determine whether the predictive weight of these units differs according to the language in which the child is learning to read. While rhyme is a unit that carries significant predictive power in English, there is little evidence of its relevance in Spanish. The purpose of the present study is to determine the predictive weight of consonant rhyme on reading accuracy, reading speed and reading comprehension from kindergarten to first grade. Ninety-four Chilean Spanish-speaking non-reader kindergarten children (49 girls and 45 boys) from low SES were tested. The results indicated that consonant rhyme has no predictive power on any of the reading skills measured. The transparency of Spanish and the main reading strategies used by children in this language are analysed as explanatory elements of the results found.