Edit:
> unless there is a warrant provided.
This element is also difficult in practice. What stops a rogue employee from taking a peek? Now you need to have strong organization controls on access, audit trails, etc. It expands the problem of private, secure chat out of the realm of "is this encryption system secure" and into the realm of "is this organization managing and auditing data access responsibly". The latter is a much harder question to answer and more prone to change over time with no notice.
Use a threshold scheme to share the warrant key among multiple independent share holders. Use enough share holders and a high enough threshold to make the odds of enough share holders going rogue or being corrupted to reveal the warrant key lower than the odds that someone will brute force the key.
In the limit you could make everyone in the country a share holder and require a large supermajority for key recovery.
> This element is also difficult in practice. What stops a rogue employee from taking a peek?
More pertinently, a warrant is not a magical guarantor that the surveillance is legitimate (nor can a backdoor be made that only works with a warrant - a warrant is not a technical barrier). If a government is already so anti-privacy that they force all their citizens to use backdoored communication, we can expect warrants to be rubber-stamped. Eventually some secret court will approve a warrant that covers an entire city or country, and it'll be renewed every two years as a routine matter.
...that's called a backdoor.
https://www.justsecurity.org/16503/security-front-doors-vs-b...
Facilitating mass surveillance of populations is the opposite of 'responsible'. It's what allows tyrannical governments to remain in power.