2001 Chevy Impala Engine stops with out warning

My 2001 Impala LS w/ aprox 122K miles recently began to stop when I'm driving it. No sputter or other warning - almost like switching the key off. It starts right back up after coming to a stop and putting it into Park. It has done it several times in the last week, however, not at the mechanic's where it spent today. I thought maybe bad gas and tried a gas additive, but that wasn't the solution. I can't go on like this.

Anyone got a clue? In my opinion it a fuel delivery problem (filter - pump?) And no, I don't know then the filter was last replaced.

Thanks in advance for your assistance folks