Yes, your employer can require you to sign a non-competition agreement. If you do not, the employer could terminate you.Note that while non-competition agreements are enforceable, courts will  restrict or cut them back if they are too long or too broad. For non-owners, non-senior executives, or non-top sales representatives, a typical enforceable non-competition will prevent the employee from working for a competitor (or going into competition him- or herself) for a period of 6 - 12 months. For "local" businesses (e.g. contractors, hair salons, realtors, etc.), it will  typically only cover a radius of from several miles to a county or three; for businesses that sell over a broader area, the noncompetition area will typically be the relevant market.