Answer by taking a quote from the following article:

Muddy Waters' birthplace and date are not conclusively known. He stated that he was born in Rolling Fork, Mississippi, in 1915, but it is believed to be more likely that he was born in Jug's Corner, in neighboring Issaquena County, in 1913. Recent research has uncovered documentation showing that in the 1930s and 1940s, before his rise to fame, the year of his birth was reported as 1913 on his marriage license, recording notes, and musicians' union card. A 1955 interview in the Chicago Defender is the earliest in which he stated 1915 as the year of his birth, and he continued to say this in interviews from that point onward.

In August 1941, Alan Lomax went to Stovall, Mississippi, on behalf of the Library of Congress to record various country blues musicians. "He brought his stuff down and recorded me right in my house," Muddy recalled for Rolling Stone magazine, "and when he played back the first song I sounded just like anybody's records. Man, you don't know how I felt that Saturday afternoon when I heard that voice and it was my own voice. Later on he sent me two copies of the pressing and a check for twenty bucks, and I carried that record up to the corner and put it on the jukebox. Just played it and played it and said, 'I can do it, I can do it.'" Lomax came back in July 1942 to record him again. Both sessions were eventually released by Testament Records as Down on Stovall's Plantation. The complete recordings were reissued by Chess Records on CD as Muddy Waters: The Complete Plantation Recordings. The Historic 1941-42 Library of Congress Field Recordings in 1993 and remastered in 1997.  In 1943, Muddy Waters headed to Chicago with the hope of becoming a full-time professional musician. He lived with a relative for a short period while driving a truck and working in a factory by day and performing at night. Big Bill Broonzy, then one of the leading bluesmen in Chicago, had Muddy Waters open his shows in the rowdy clubs where Broonzy played. This gave Muddy Waters the opportunity to play in front of a large audience. In 1944, he bought his first electric guitar and then formed his first electric combo. He felt obliged to electrify his sound in Chicago because, he said, "When I went into the clubs, the first thing I wanted was an amplifier. Couldn't nobody hear you with an acoustic." His sound reflected the optimism of postwar African Americans. Willie Dixon said that "There was quite a few people around singing the blues but most of them was singing all sad blues. Muddy was giving his blues a little pep."  Three years later, in 1946, he recorded some songs for Mayo Williams at Columbia Records, with an old-fashioned combo consisting of clarinet, saxophone and piano; they were released a year later with Ivan Ballen's Philadelphia-based 20th Century label, billed as James "Sweet Lucy" Carter and his Orchestra - Muddy Waters' name was not mentioned on the label. Later that year, he began recording for Aristocrat Records, a newly formed label run by the brothers Leonard and Phil Chess. In 1947, he played guitar with Sunnyland Slim on piano on the cuts "Gypsy Woman" and "Little Anna Mae". These were also shelved, but in 1948, "I Can't Be Satisfied" and "I Feel Like Going Home" became hits, and his popularity in clubs began to take off. Soon after, Aristocrat changed its name to Chess Records. Muddy Waters's signature tune "Rollin' Stone" also became a hit that year.

what year did he move to chicago?
1943, Muddy Waters headed to Chicago