This is an open label, single center study to assess safety, feasibility, and efficacy of Cultivated Autologous Limbal Epithelial Cell (CALEC) grafts in 24 patients with unilateral limbal stem cell deficiency. The first 3 participants enrolled will receive the study treatment, CALEC, to assess for safety and feasibility. Subjects 4-24 will be randomized to either the study treatment, CALEC, or to the standard treatment for LSCD, which is conjunctival limbal autograft (CLAU) in a 2:1 ratio.