In this multicenter trial, physicians will evaluate multiple dosage levels of sodium phenylbutyrate to determine the maximum tolerated dose (MTD), or the highest dose that can be safely given to children with SMA type I. The initial dosage tested will be 500 mg/kg/day. Depending upon tolerability, subsequent groups may receive dosages of 675, 900, or 1200 mg/kg/day. Blood levels of SMN mRNA and protein will also be measured to determine whether sodium phenylbutyrate can increase the amount of these two biomarkers in the blood. Up to 24 children will be enrolled in the study, and will be on sodium phenylbutyrate for 12 weeks. The MTD will be determined based on safety data from Day 0 through the Day 29 visit. Participants will continue to be monitored for safety and SMN mRNA and protein levels through the 12 week study drug administration period.