No, unless you can show "undue hardship." The law in effect on the date the bankruptcy is filed controls. In re Shaw, Case No. 13-03251, U.S. Bankruptcy Court, SD Texas 2015.
Private student loans were dischargeable in bankruptcy prior to BAPCPA, the Bankruptcy Abuse Prevention and Consumer Protection Act of 2005. Under current law, if the private student loans are qualified educational loans, you must filed an adversary proceeding and prove "undue hardship" during your bankruptcy case, in order to have them discharged. It can be a very difficult burden.