This work, written for the San Francisco Symphony in 1986 and premiered that year with the composer conducting, is the third and last example of Lutoslawski's "chain-form" pieces, though the technique would persevere into other, later works. It had been preceded by Chain 1 for chamber ensemble, written in 1983 for the London Sinfonietta, and Chain 2 (1985), a "dialogue for violin and orchestra" premiered by Anne-Sofie Mutter to both critical and audience acclaim.

Chain 3 is a tight and focused composition in three parts which flow into one another; it is perhaps the most expressively pure of the three. Lutoslawski's "chain form" denotes a technique in which small musical ideas of contrasting character are overlapped upon one another like links in a chain, creating a dynamic yet fluid sense of forward movement. (In Chain 2 the dialogue between orchestra and soloist gives the form a dialectical character, while in this work the flow is more narrowly driven.) The other innovation for which Lutoslawski is well known came from an encounter with the work of John Cage in 1958. His adaptation of Cage's indeterminate musical instructions came to be called aleatoric counterpoint, in which individual players—only in specially determined parts of a composition—could repeat at will short musical motives specifically outlined by the composer, creating the illusion of complex linear counterpoint.

The first section of Chain 3 uses both these techniques to powerful effect. After a brief orchestral call to arms—a typical Lutoslawskian device—a series of twelve separate ideas are presented, all of which use the aleatoric "ad libitum" process: a section for three flutes and bells is undermined by music for four solo basses, which then overlap with music for solo violins, the violins connecting with the entrance of clarinets and xylophone, etc. Each mini-section, with its small motives of strictly limited pitches, sounds somewhat improvisatory, but the differing expressive characters of these sections, allied with brilliant and subtle changes in orchestration, build up a sense of momentum which reaches a climax in a roiling passage for general winds.

In the second large section, the chain technique is no longer immediately audible, but drives the form nonetheless. It begins with a vigorous orchestral tutti, built from material of the first section but strictly notated in traditional fashion. Gradually a violin melody, marked cantabile, emerges as the music's most urgent impulse; its line is sometimes broken up by skittish runs of sixteenth notes. Various diversions—rich pizzicato chords, glissando strings, a lyrical moment for the flute—occasionally interrupt the melody's pace, but eventually it reaches a thrilling climax, breaking apart in a long stretch of aleatoric music for the winds and brass. A consciously doctrinaire fugato for the strings attempts to crawl up from the dust, and when joined by the rest of the orchestra results in a jarring fff chord based in A major: it is a rare bit of tonality in what is a richly chromatic composition. But after three brutal staccato chords, a group of slowly sliding cellos winds the work down with an unexpected sigh.

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