ESPN is based out of Bristol, Connecticut. And Connecticut is considered an “at-will” employment state. LawNewz has discussed and analyzed at-will employment in the past. (See here. And here.) But to make a long story short, at-will employment is a soft euphemism for: employers can hire and fire more or less whenever they feel like it.
In Connecticut, “at-will” employment is considered a common law “right” recognized by the courts and available to both employers and employees. Leaving aside the real world implications of private employers’ effective dictatorship over their employees, this means that if ESPN decided to fire Hill, they could do so–for almost any reason.
This doesn’t mean, however, that ESPN could escape liability for firing Hill if they fired her based on her speech.