Sadly for a game that features great potential for co-op play, The Last of Us will only be a singleplayer story focused campaign. There will however be some form of multiplayer component in the game which is still being kept close the chests of the developer.
In an interview with Gaming Examiner game director Neil Druckmann said that The Last of Us will “not [have] co-op within the main campaign.”
“We are supporting multiplayer with The Last of Us [but we’re] not ready to talk about the details of how multiplayer will be implemented.”