What? If you have a grievance HR or legal is the last place you should turn to as an employee. No matter what your position is it basically starts the process of getting yourself fired.
HR's primary mission is to protect the company from its employees.
No- HR's goal is to protect the company's best interests. Sometimes this coincides with an employee's own best interests, and sometimes this goes against it.
And emailing the CEO won't? I recall some stories about the people at amazon who emailed Bezos regarding their difficulties at work..