Open-source alternatives to Intercom

Chatwoot is open source: free to download and run on your own server. Intercom costs from $29 a month.

Chatwoot

Open core (MIT) · Open-source customer support inbox, an alternative to Intercom and Zendesk

Chatwoot brings live chat, email, WhatsApp, social media and more into one support inbox, with a help centre and an AI agent called Captain.

The core is open source under the MIT licence and free to run on your own server; some enterprise features need a paid licence.

Free to use, not free to run. The licence costs nothing, but self-hosting needs a server (often $5 to $40 a month) and someone to install updates and keep backups.
Open core means the main product is open source but some features, usually for larger teams, need a paid licence.
Hosted versions exist for many of these, run by the makers. They cost money but save the upkeep, and you can still move to your own server later.
Licences differ. MIT and Apache allow almost anything. GPL and AGPL require you to share changes you make to the code; for normal business use, that rarely matters.