As per the Spring '16 release notes, Chatter Messenger: Retiring in Spring ’17 and unavailable and no longer supported for new Salesforce organizations created after Spring '16.
For existing organizations which have been created prior to Spring '16 see:
How do you enable Chatter Messenger?
Why I can not see Chatter Messenger for my organization with all supported browsers?
What this means for you:
Chatter Messenger isn’t available in Salesforce orgs created Spring ’16 or later.
If you enabled Chatter Messenger before Spring ’16, it remains available in your Salesforce org. Salesforce will no longer support Chatter
Messenger as of Spring ’17.
For existing organizations which have been created prior to Spring '16 see:
How do you enable Chatter Messenger?
Why I can not see Chatter Messenger for my organization with all supported browsers?
