More to the point, why are you creating it in the first place?
It's quite hard to do - if your string always starts with SELECT and has nothing after the last comma, then it's not too bad: just strip off the SELECT, split the remainder on the comma, and throw away the duplicates. Then just put it all back together.
string str = "SELECT a.LastUpdate,a.AgreementID,a.AgreementID,b.CustomerID,a.AgreementID,";
string justTheList = str.Substring(7);
string[] elements = justTheList.Split(new char[] { ',' }, StringSplitOptions.RemoveEmptyEntries);
str = "SELECT " + string.Join(",", elements.Distinct());
But...it'd be a lot tidier to do it when you generate the string in the first place...