This study will enroll subjects with qualifying limbal stem cell deficiency (LSCD). All subjects will receive CSB-001 investigational drug in either one or both study eyes. The study is comprised of two identical phases (Dosing Phase I and II) of test article dosing separated by a 31- to 40-day period, the Dosing Holiday, where no test article is administered. Dosing Phase II is followed by an observational, noninterventional phase (Observation Phase).

Inclusion Criteria:

• Have an area of the central 5 mm zone of cornea affected, presence of at least one clinical sign observed by slit-lamp examination with white light and/or cobalt blue light, fluorescein, and a Wratten filter, and at least one clinical sign observed with AS-OCT.
• If dosing with Acthar at time of Screening Visit, must have a history of stable dosing for approximately 8 weeks, plan to maintain the same Acthar treatment dose and regimen, and have demonstrated little to no improvement in severity of LSCD.
• Sponsor written confirmation of qualifying LSCD diagnosis.
• Inflammation associated with LSCD or other non-infectious inflammation that will not interfere with subject's participation.

Exclusion Criteria:

• Any active ocular infection (bacterial, viral, fungal, or protozoan) in either eye.
• Ocular surgery within 30 days of Day 0 where investigator assesses that healing is not considered complete/stable.
• Planned ocular surgery on or before Week 20 visit.
• Presence or history of any ocular or systemic disorder, condition, or procedure that might hinder the efficacy of the study treatment or its evaluation, or could interfere with the interpretation of study results, in the opinion of the investigator.

Note: Other inclusion/exclusion criteria apply.