An important tendency in Proto-Slavic - a tendency that also operated throughout the Common Slavic period (ca. 300 to 1000 CE) and was the direct cause of the first palatalization - was so-called intrasyllabic synharmony. Such intrasyllabic synharmony was violated if a velar consonant occurred before a front (palatal) vowel, because a velar is articulated in the region of soft palate (velum), in the back part of the roof of the mouth, and front vowels, of course, in the front part of the mouth. Speakers resolve this articulatory opposition by adapting (assimilating) the articulation of the velar consonant to the front vowel, relocating it to the region of the front soft palate (palatum) - i.e.: it becomes palatalized.
This phenomenon occurs very commonly in the phonetic history of languages. Velar palatalization before front vowels has also marked (for example) the evolution of almost all modern Romance languages.
Inherited velars *k (< PIE *k, *kʷ) and *g (< PIE *g, *gʰ, *gʷ, *gʷʰ) change before Proto-Slavic front vowels *e/ē, *i/ī (PIE *e/ē, *i, *ey/ēy, *ew/ēw > OCS e/ě, ь, i, 'u), and also before the palatal semivowel *j:
The Proto-Slavic velar fricative *x, which was absent in PIE and arose primarily from PIE *s by means of the RUKI law or from word-initial PIE #sk- (as well as from Germanic and Iranian borrowings), changed in the same environment as:
The effect of the first palatalization is also evident on Germanic loanwords. Compare:
Even though it is commonly stated in the literature that the result of first palatalization were consonants */č/, */ž/, */š/, there is no certain evidence that that process was indeed finished by the 600 CE.
There is also some disagreement on whether Proto-Slavic velars became affricates before front vowels and before */j/; at first sight, it seems likely that palatalization of velars was an older process than palatalization before */j/.
Many linguists think that the transition *kj > *č, *gj > *ž, *xj > *š occurred simultaneously with the changes *sj > *š, *zj > *ž, i.e. together with changes otherwise known as the Common Slavic iotation (or yodization). However, that change is in fact Common Slavic (post-Proto-Slavic), which is obvious e.g. from the adaption of Romance toponyms in the Adriatic, to which Slavs subsequently spread well after the 5th century, when first regressive palatalization is usually dated. Compare:
On the other hand, from a purely phonetic viewpoint, it's very hard to believe that velars might have been unpalatalized before *j by the time they palatalized before *e and *i.
That being said, the first palatalization must have proceeded gradually:
The most economic interpretation is that there was no difference in Proto-Slavic of *k and *g before *j, and before *e, *i, i.e. that the pronunciation was *kj, *gj. *j was then lost after palatalized velars (or affricates) in Common Slavic period of iotation of other consonants.
With that in mind, consonants */č/ and */ž/, which are usually reconstructed in the phonemic inventory of Proto-Slavic in the literature, were likely to be just phonologically predictable allophones of */k/, and */g/, and have remained such until conditions were met after the 600 CE for their appearance behind back vowels as well. Similarly, *š which resulted by the application of RUKI law was an allophone of */s/ after *r, *u, *k, *i, but when *š emerged from Proto-Slavic *sj, the opposition between *š and *s became phonological, i.e. */š/ became phonemicized.
The results of the first palatalization were the same in all Slavic languages, which shows that it probably took place before the migration of Slavs into their historical settlements, and that means probably before 500 CE. As previously mentioned, this palatalization also operated on Germanic loanwords, which the proto-Slavs probably borrowed before or not long after the Huns disrupted the Gothic hegemony (c. 375 CE). This all shows that it operated throughout the 5th century.
Further evidence on that date comes from the toponymy and the hydronymy of the upper Dnieper river, which Slavs colonized probably in the latter half of the 5th century. Before their arrival, that region was populated by Baltic speakers, and the Baltic river names such as Vilkesà, Akesa, Laukesà and Merkys yielded Russian equivalents Volčesa, Očesa, Lučesa, and Mereč'. This shows that the palatalization was operable in the latter half of the 5th century.
By the time Slavs reached the south of Greece and the Adriatic coastline, in the 6th and the 7th centuries, the first palatalization no longer operated. That can be seen from the fact that Slavic words were borrowed into Middle Greek in palatalized form, and also from the fact that Romance toponyms on the Adriatic undergo the second, not the first palatalization.
On the basis of this data, and on the basis of the fact that for the sound change to be complete at least three generations are needed, i.e. c. 75 years, Arnošt Lemprecht concluded that the first Slavic palatalization operated approximately from 400 to 475 CE, ±25 years.