The only way to have secure chat is to use end-to-end encryption, which means that only the communicating users can read the messages.
For more secure communication, we recommend using, in order of preference:
- Signal
- WhatsApp / Telegram
For more secure communication, we specifically recommend avoiding:
- Facebook Messenger
- SMS
- Any other chat program not mentioned above
Some applications support automatically deleting chat messages after a given time period (such as an hour or a week). Consider enabling this feature for sensitive discussions.
Signal
Signal has end-to-end encryption for individual chats and group chats.
It supports automatically removing messages.
WhatsApp has end-to-end encryption for individual chats. 
: Does it support e2e for group chats?
- Make sure to disable unencrypted cloud backup.
- Note that WhatsApp is owned by Facebook.
Telegram
Telegram has optional end-to-end encryption for individual chats. It does not support end-to-end encryption for group chats.
It supports automatically removing messages in individual chats, but not in group chats.
Element
Element has end-to-end encryption for individual chats and group chats.
It is unfortunately somewhat complex and not suitable for use by non-technical users at this time.
SMS
We recommend avoiding SMS for any sensitive discussions.
SMS can be easily intercepted by an adversary, and is readily available to your phone company and the state.
Facebook Messenger
We recommend avoiding Facebook Messenger for any sensitive discussions.
There is reason to believe that Facebook stores messages indefinitely on their servers, even if you request that they are deleted. All messages are readily available to Facebook and the US government.