Using json_build_object (Postgres 9.4) to map each username to an array of posts:

    SELECT 
      json_build_object(
        u.username,
        (SELECT json_agg(p) FROM posts p WHERE u.id = p.user_id)
      )
    FROM users u

Output:

    [
      {"chuck": null},
      {"blair": [
        {"id": 1, "markup": "hello"},
        {"id": 4, "markup": "world"}
      ]},
      {"serena": [{"id": 5, "markup": "testing"}]}
    ]

At least I think you were trying to do that.