Can bad kamma be overcome in one lifetime

If there is a puthujjana who has led a life full of the major and minor defilements till about 40 years of age, suddenly turns around, starts leading a totally celibate life and also observes the rest of the major five precepts strictly, maintaining a strict meditation schedule even while still being a householder, does he stand a chance of getting nibbana in this very lifetime? Or, does he have to take rebirth/s and suffer the consequences of his bad kamma before he can aspire to Arahathood?