The Chromatic Mediant

A chord of the tonic’s own quality whose root sits a third away, right next to the tonic chord. The reader only calls it once every simpler reading has been ruled out.

The rule, as the reader applies it

In a key whose tonic chord is major or minor: the tonic chord, followed by a chord of the tonic chord’s own quality a minor third, major third, minor sixth or major sixth above the tonic, with at least one note outside the key, and not in the parallel key either, and not followed by a chord whose root is a fifth below it.
In a key whose tonic chord is major or minor: a chord of the tonic chord’s own quality a minor third, major third, minor sixth or major sixth above the tonic, with at least one note outside the key, and not in the parallel key either, followed by the tonic chord.

Where it fires: three times in three lines

Every line in this site’s corpus where the chromatic mediant fires: the line, the key it is read in, the chords the move covers and their numerals.
Line	Read in	Chords	Numerals	Line from
C E C	C major	C E	I–III	as printed in Chromatic mediant (Wikipedia)
C A C	C major	C A	I–VI	as printed in Chromatic mediant (Wikipedia)
Am Cm Am	A minor	Am Cm	i–biii	as printed in Chromatic mediant (Wikipedia)

The move as declared here was read from Chromatic mediant (Wikipedia), which prints it as E, A, Eb and Ab in C major.

Spotting it

The reader looks at a chord right next to the tonic chord in the line, before it or after it, whose root sits a minor or major third above or below the tonic and whose triad has the tonic's own quality: major beside a major tonic, minor beside a minor one. At least one of its notes must be outside the key. In C major the chords with that shape are E, A, Eb and Ab major; in A minor they include C minor.

What is ruled out first

The source for this move quotes Sorce: before calling anything a chromatic mediant, rule out borrowing, then rule out a chord leaning on the next one. The reader does both. A chord whose every note belongs to the parallel key on the same tonic is borrowed, and it is read as bIII or bVI instead; that removes Eb and Ab in C major, so in C Ab C the Ab is the flat six and this rule stays silent. A chord followed by one whose root is a fifth lower is leaning on it, so in C E7 Am F G C the E7 is read as V of vi.

In the table

What is left are the chords from outside both keys. In C E C the E major reads III with G# outside the key; in C A C the A major reads VI with C# outside it. In A minor, Am Cm Am puts C minor between two tonic chords. Every numeral here is counted from the major scale on the tonic, so the C minor chord reads biii, where the source, counting from the minor scale, writes iii. The span covers the chord and the tonic chord beside it.