If you are referring to a vaginal birth...it's not likely. After having 4 c-sections your risk of uterine rupture has increased significantly. It would really depend on your doctor and how long ago your c/s were.
Usually they will only let you attempt a VBAC after having your first c-section. Like LosingMyMind said, you are a great risk for uterine rupture that could kill you and your baby.
The ACOG actually released less restrictive guidelines on vbacs the middle of last year. They now advocate trial VBAC even after a 2nd c/s depending on circumstances and health. However, after having had 4 it is highly unlikely ANY doctor would be willing to forgo the risks to attempt VBAC.