I searched on Wikipedia and Google but can't find a translation (apart from the title, La kronikoj de Narnio). It surprises me, since it thought it was as culturally important as, for instance, the Lord of the Rings and The Hobbit, which have a translation.
Short answer: There is probably no translation of this book.
Long answer: There is no automatism as regards translations of important books into Esperanto. While there are many works of world literature available as translations, others are simply lacking, just think of Homer's Iliad and Oddyssey, which are quite more important than The Chronicles of Narnia.
Please call into mind the conditions of book production in Esperantujo: You don't only need a competent translator with enough free time and the will to do the work for free (as you usually don't earn any money by publishing Esperanto books), you also need a publisher - and in case of modern books the permission to translate and publish at all. As commercial publishers or authors usually don't give away their copyright without fees, many manuscripts of translated books may even be ready, but cannot be published in a legal way yet (I know such cases), so they either "rest in the drawer" or circulate as pirate translations (like the first Harry Potter novel). Cf. also this question on StackExchange.
(Dear native speakers, please correct my English :-))