He began his career in Zack Whyte's territory band in Ohio in 1928. In the early 1930s he moved to New York and found work as an accompanist to Ethel Waters, Adelaide Hall, and Clarence Williams. He also visited Boston for the first time with a traveling show headlined by comic actor Stepin Fetchit. In late 1933 he went to Europe with the Willie Lewis Orchestra and toured Europe with them and the following year he recorded with Louis Armstrong in Paris. Later he and Bill Coleman led the "Harlem Rhythm makers". Chittison and trumpeter Bill Coleman left Lewis in 1938 and formed a band that worked extensively in Cairo and traveled as far east as India. In October 1959, Chittison arrived in Boston and was employed as the resident pianist at the Red Garter bar in the Lenox Hotel. He then moved to the Mayfair Lounge, in Bay Village. His stay in Boston lasted two years. Chittison was one of the earliest and most important ambassadors of American jazz in Europe. As it is shown by many of his early recordings of 1933-1941, he was also a formidable virtuoso, with a piano technique very close to Art Tatum's.
The radio program Casey, Crime Photographer featured Chittison playing jazz piano at the Blue Note Club, Casey's informal headquarters. A later series of the same show featured the Teddy Wilson Trio in the same setting.