The laryngeal theory is a widely accepted scientific theory in historical linguistics positing that the Proto-Indo-European (PIE) language included a series of consonants that left no direct consonantal descendants in languages outside of the Anatolian branch. It was first proposed by the Swiss linguist Ferdinand de Saussure in 1878 to explain apparent irregularities in morphophonological patterns in daughter languages. At the time no direct evidence for the existence of such sounds was available; however, the theory allowed for a better reconstruction of PIE ablaut and root. This changed in 1927 when a Polish linguist Jerzy Kuryłowicz discovered that a sound transcribed as ḫ in the newly deciphered ancient Indo-European Hittite language appears in many of the places that the laryngeal theory predicted.

Subsequent scholarly work has established a set of rules by which an ever-increasing number of reflexes in daughter languages may be derived from PIE roots. The number of explanations thus achieved and the simplicity of the postulated system have both led to widespread acceptance of the theory.

The reconstructed sounds are traditionally called "laryngeals" and are known to have been consonants, most likely fricatives; however, their exact place of articulation is debated. In its most widely accepted version, the theory posits three laryngeal phonemes in PIE. They are represented abstractly as *h₁, *h₂, and *h₃ (also written *H₁, *H₂, *H₃ or *ə₁, *ə₂, *ə₃, among other notations). Aside from some direct consonantal reflexes in the Anatolian branch, in other branches through regular sound changes they were turned into vowels or were lost entirely, but could influence the place of articulation or length of neighboring vowels.

The beginnings of the theory were proposed by Ferdinand de Saussure in 1879, in an article chiefly demonstrating that *a and *o were separate phonemes in PIE.

In the course of his analysis, Saussure proposed that what had then been reconstructed as long vowels *ā and *ō, alternating with *ǝ, was an ordinary type of PIE ablaut. That is, it was an alternation between e grade and zero grade like in "regular" ablaut (further explanations below), but followed by a previously unidentified element. This element accounted for both the changed vowel colour and the lengthening (short *e becoming long *ā or *ō).

So, rather than reconstructing *ā, *ō and *ǝ as others had done before, Saussure proposed *eA alternating with *A and *eO with *O, where *A and *O represented the unidentified elements. Saussure called them simply coefficients sonantiques, which was the term for what are now in English more usually called resonants; that is, the six elements present in PIE which can be either consonants (non-syllabic) or vowels (syllabic) depending on the sounds they are adjacent to: *y, *w, *r, *l, *m, and *n.

These views were accepted by a few scholars, in particular Hermann Möller, who added important elements to the theory. Saussure's observations, however, did not achieve any general currency, as they were still too abstract and had little direct evidence to back them up.

This changed when Hittite was discovered and deciphered in the early 20th century. Hittite phonology included two sounds written with symbols from the Akkadian syllabary conventionally transcribed as ḫ, as in te-iḫ-ḫi 'I put, am putting'. This consonant did not appear to be related to any of the consonants then reconstructed for PIE, and various unsatisfactory proposals were made to explain this consonant in terms of the PIE consonant system as it had then been reconstructed.