1590s, "the science of time," from French chronologie or directly from Modern Latin chronologia; see chrono- + -logy. Related: Chronologer (1570s). Meaning "particular statement of the supposed order of certain past events" is from 1610s.
compound adjectival word-forming element, usually interchangeable with -ic but sometimes with specialized sense (such as historic/historical, politic/political), Middle English, from Late Latin -icalis, from Latin -icus + -alis (see -al (1)). Probably it was needed because the forms in -ic often took on a noun sense (for example physic). Forms in -ical tend to be attested earlier in English than their twins in -ic.
<a href="https://www.etymonline.com/word/chronological">Etymology of chronological by etymonline</a>
Harper, D. (n.d.). Etymology of chronological. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/chronological