During the 1920s Paul Hindemith wrote one of his most important series of works, seven compositions with the designation "Kammermusik" ("chamber music"). Most of entries in this series are in fact concerti for a solo instrument and chamber orchestra, in each case comprising a unique ensemble. In the present work, Hindemith employed as accompanying body to the solo cello a group consisting of flute, oboe, clarinet, bassoon, horn, trumpet, trombone, cello, and double bass. The composer himself conducted the premiere in Bochum, Germany in April, 1925, with his brother Rudolf as cellist.

The technique and form of Kammermusik No. 3 can be most accurately described as generated through principles of neo-Classicism and counterpoint. The work is primarily tonal, though the chromatic, often dissonant harmonies are plainly of Hindemith's own bracingly astringent language. In the first movement, Hindemith introduces the instruments successively: the cello states a ten-measure theme, which is taken up by the other strings. The theme is then taken up by the woodwinds, while the strings assume a supporting chordal role; then the trumpet assumes the fore. These soloistic entrances foreshadow the relationship of the instruments throughout the movement; the cello is treated merely as the most prominent voice in a true chamber dialogue. The second movement shares much of the same quality, though with an added measure of brilliance for the cello. The third movement is intimate in tone, while the two-minute finale serves as an extended coda to the work.

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