This trial is investigating the effects of stem cells from the patient's own fat in the treatment of chronic spinal cord injury. The trial is being conducted at the Korea University Anam Hospital in Seoul and plans to recruit 15 participants. The fat stem cells will be injected into the fluid surrounding the spinal (intrathecal injection) three times over approximately two months. Participants will be monitored for complications and assessed for changes in neurological and sensory function. The trial is expected to complete in December 2013.