As a former day care PreK teacher and mother, I think that if you are confident in the facility and the staff, then you are ahead of the game. At three, your child is at the perfect age to start learning how to socialize with other children, and to also begin to learn the basics for Kindergarten. Also, it will be a great way for your child to build up their immities to childhood illnesses. We maybe get one head cold all year in the house now.
I've seen many parents stuggle with sending their children off into the arms of strangers. I had a hard time putting my son in day care, and I worked there! It'll take some adjustment, but like I said in the beginning of my answer, if you are confident in the staff, then you are in a great place and so is your child.