Chin or Neck Liposuction is a safe procedure when performed by an experienced, competent Board Certified Plastic Surgeon.
However ALL surgical procedures, no matter how minor, carry some risk of complication.
While complications of Chin or Neck Liposuction are rare they can include bleeding, infection, skin irregularity, fluid accumulation, and inadequate result among others.
The most important thing is for you to find an expert surgeon whom you trust and feel comfortable with. Referrals from friends who have had good results are an important source of information.
See 2 or more Board Certified Plastic Surgeons who do Liposuction. Ask them to discuss potential complications, see photos of their results and if possible speak to patients who have had the procedure.
Trust you instincts, if you are uncomfortable, see a different doctor.