Very recent observations of the ^ { 6 } Li isotope in halo stars reveal a ^ { 6 } Li plateau about 1000 times above the predicted BBN abundance . We calculate the evolution of ^ { 6 } Li versus redshift generated from an initial burst of cosmological cosmic rays ( CCRs ) up to the formation of the Galaxy . We show that the pregalactic production of the ^ { 6 } Li isotope can account for the ^ { 6 } { Li } plateau observed in metal poor halo stars without additional over-production of ^ { 7 } { Li } . The derived relation between the amplitude of the CCR energy spectra and the redshift of the initial CCR production puts constraints on the physics and history of the objects , such as pop III stars , responsible for these early cosmic rays . Consequently , we consider the evolution of ^ { 6 } Li in the Galaxy . Since ^ { 6 } Li is also produced in Galactic cosmic ray nucleosynthesis , we argue that halo stars with metallicities between [ Fe/H ] = -2 and -1 , must be somewhat depleted in ^ { 6 } Li .