According to The Jewish Daily Forward, its use as an amulet originates in 18th century Eastern Europe.
Chai as a symbol goes back to medieval Spain. Letters as symbols in Jewish culture go back to the earliest Jewish roots, the Talmud states that the world was created from Hebrew letters which form verses of the Torah. In medieval Kabbalah, Chai is the lowest (closest to the physical plane) emanation of God.
According to 16th century Greek rabbi Shlomo Hacohen Soloniki, in his commentary on the Zohar, Chai as a symbol has its linkage in the Kabbalah texts to God’s attribute of ‘Ratzon’, or motivation, will, muse.
The Jewish commentaries give an especially long treatment to certain verses in the Torah with the word as their central theme. Three examples are Leviticus 18:5 וָחַי בָּהֶם ‘Chai Bahem’, ‘and you shall live by [this faith]’ (as opposed to just doing it), this is part of the section dealing with the legacy of Moses Our Teacher following his death. Deuteronomy 30:15 רְאֵה נָתַתִּי לְפָנֶיךָ הַיּוֹם, אֶת-הַחַיִּים וְאֶת-הַטּוֹב, וְאֶת-הַמָּוֶת, וְאֶת-הָרָע. “Verily, I have set before thee this day life and good, and death and evil, in that I command thee this day to love the LORD thy God, to walk in His ways, and to keep His commandments and His statutes and His ordinances; then thou shalt live.” There is nary an ancient Jewish commentator who does not comment on that verse. The Shema prayer as well speaks of the importance of Chai, to live and walk in the Jewish cultural lifestyle.