If the vehicle starts, rule out the starter.
It can be an alternator issue, but it could be some other things. For example - does it start right back up? If so, then the battery still has power, which leads me to believe the alternator is at least doing something - if not working just fine.
If it is flat dead and your battery has no crank left in it...first check the battery. A faulty battery that will not hold a charge can also influence a stall.
The total other side of things is that you could have an engine performance issue. Your fuel system may not be supplying enough fuel. Your air intake may be allowing too much air in - either from a vacuum leak or an air intake leak. Your ignition system may be losing spark intermittently.
So, as you can see, you have a wide open spectrum of possible failures occurring. I recommend a solid tech near you has a look
There's a link you can use to find some shops near you.