- Are you looking for ArchiveTeam's IRC?
Internet Relay Chat (IRC) is an old chat protocol, being designed in 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 networks 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 network aggregators
There are a few IRC network aggregators, but the biggest one is probably irc.netsplit.de, which also scrapes channels, their historical topics and number of users.
There are a lot of sites providing quotes from IRC channels.
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, many channels have a notice about public logs in their topic and some log servers are still available online. The IRC Logs project aims to capture them.
(Incomplete) List of IRC Server URLs