  In this work we construct sequences of locally recoverable AG codes arising
from a tower of function fields and give bound for the parameters of the
obtained codes. In a particular case of a tower over $\mathbb{F}_{q^2}$ for any
odd $q$, defined by Garcia and Stichtenoth in [GS2007], we show that the bound
is sharp for the first code in the sequence, and we include a detailed analysis
for the following codes in the sequence based on the distribution of rational
places that split completely in the considered function field extension.
