According to Official Guinness Records,
The fastest marathon on crutches (one leg) is 5 hr 37 min 43 sec and was achieved by Larry Chloupek II (USA) at the Washington D.C. Rock and Roll Marathon in Washington D.C., USA, on 16 March 2013. Larry Chloupek II has been an amputee since the age of 7, having lost his leg to bone cancer.
For a complete list of 2013 records, please visit 2013 Guinness Records in United States.