- Are you looking for ArchiveTeam's IRC?
Internet Relay Chat (IRC) is an old chat protocol, being designed and 1988. IRC clients are simple and available for every platform imaginable, including your old Nintendo DS. IRC is fully decentralized, with anybody being able to run a server. There are numerous large servers with their own histories. With the advent of modern chat platforms that are more mobile-friendly among other advantages, IRC usage has been on the decline, and lately (2019) it is being abandoned even by techie folks.
IRC server aggregators
There are a few IRC server aggregators, but the biggest one is probably irc.netsplit.de, which also scrapes channels, their historical topics and number of users.
IRC servers typically do not provide logs. Clients usually keep local logs of chats, however, unless run on a reliable server running 24/7 those logs will contain blind spots.
There is an implicit agreement between IRC participants to not publish IRC logs. However, some channels have a notice about public logs in their topic. Some logs are available online, for example:
List of IRC URLS