This is an 1968 house with AL wiring. All of the outlets are new and AL compatible with anti-oxidizer paste. Starting with the first box, I pig tailed each neutral (white) wire together to see if I had a bad outlet. I went from box to box and when I came to the last box, the tester still read open neutral! This run has no switches or lights, only outlets. I also made sure that no bare ground wire was in contact with a neutral connection. All connections are tight. How can I be sure if I don't have a bad outlet, and if that's even the problem? Just replaced the breaker as well. So I am at a complete loss! Thanks in advance.

If your problem showed up in the outlet box closest (electrically) to the panel, then your problem is most likely in the main panel. Or maybe there is a junction somewhere on the neutral in that home run that is bad. A bad neutral will show 120v to ground anywhere "downstream" (farther away from the panel) of the break. I have found more open neutrals right at the neutral bar in the panel than any other single location (like back of an outlet or wire nut). Even if the conductor is in the hole in the bar, if it isn't tight it can cause the problem. Too many conductors under one screw will easily do it.

<rant> The ones that make me mad are when both the neutral and ground conductor are under the same screw. You loose both at the same time that way with no safety left. If only those perpetrators would be the ones that get the zap! NEVER put neutrals and grounds under the same screw. </rant>

You mentioned "tester" Exactly what type of tester are you using? Did you do some re-wiring which made this happen?
How does a 42 year old house have new receptales? By pigtailing the wires you effectively bypass any bad receptacle. I'd suspect a break in the wire between the panel and the first connection, whether it be the first outlet or a junction box. But start at the panel, with due caution of course. One more thing... are you sure the breaker is good? IF you aren't using a multimeter you probably aren't getting the whole story.

If the neutral had been in contact with ground, although incorrect, Your tester would not show a problem as both are at the same potential.
I would check the neutral at the panel as mentioned. You can tell which neutral by turning off breakers/pull fuses to find which is that circuit, then follow that hot, and see which neutral goes with it. Check the connection.
I would check the outlet closest to the Panel, if a wire is nicked while stripping it can break while twisting together and go unnoticed.
You could separate the grounds, then with a tester, check for power between the hot and ground, which ever has power, is the first one.
Over the years of heat/cold, the aluminum can get brittle.
Good luck

Thanks for your answers!

Think I'm going to have to call an electrician.