The optic cup houses multipotent retinal progenitor cells that proliferate and differentiate to form the mature retina, containing five main types of neurons and a single glial cell type, the Müller cell. Progenitors of the zebrafish optic cup generate clones that vary regarding the number and types of neurons, a process we previously showed could be described by stochastic models. Here, we present data indicating that each retinal progenitor cell, in the 24 hrs post-fertilization optic cup, is predestined to form a single Müller cell. This striking fate assignment of Müller cells reveals a dual nature of retinal lineages where stochastic mechanisms produce variable numbers of neurons while there is a strong deterministic component governing the formation of glia cells. A possible mechanism for this stereotypic fate assignment could be the maintenance of a clonal backbone during retina development, which would be similar to invertebrate and rodent cortical neurogenesis.