Apple's iMessage is end-to-end encrypted, which means it's safe for 99% of communication. The company has testified repeatedly in court that if the government were to subpoena a customer's iMessages, Apple wouldn't be able to comply because it's encrypted data.
"Encryption is a byproduct because Apple could do it to make it safe," Will Strafach told TI. "I don't think it's meant to be a private secured thing as a primary goal."
Strafach also recommends Signal as a good encrypted chat app. It's open-source, which means it's not controlled by any one company and it's encryption methods are available for anyone to examine.
But only use something like Signal if you're seriously concerned about being spied on.
"Unless you have a reason to be surveilled, you're probably not going to have to worry a lot about this," Strafach cautioned.