This pilot clinical trial studies whether unilateral group D retinoblastoma, or retinoblastoma affecting one eye that has spread to the inner jelly like part of the eye, can be treated with a new technique for delivering chemotherapy directly into the blood vessel that supplies the affected eye. This new technique is called intra-arterial injection. This may give children with unilateral retinoblastoma a lower chance of needing surgery to remove the eye and reduce the amount of treatment side effects.