Chwatal was born in Rumburk, Bohemia (in the modern Czech Republic). He was the son of an organ builder, who gave him piano lessons as a child. From 1822 to 1832 he worked as a music teacher in Merseburg, where he created his first compositions. From 1835, he worked as a music teacher in Magdeburg. In the 1850s, he travelled with Christian Friedrich Ehrlich to the Institute für Gemeinschaftlichen Clavierunterricht (Institute for Community Piano Lessons).
He composed numerous pieces of music. However, these compositions have had a reputation as lighter, popular music. The German music critic Robert Schumann called them "Stübchenmusik" (parlour music).