How can I measure the noise on my AC mains with a 2ch oscilloscope?

Jason you make a good point !

OP.  While that is a nice experiment, it isn't really necessary.  Nobdy has good quality power coming into their home today.  Too many non-synchronous loads on the line that mangle the sine wave.  My power generally runs 4% thd or so.  

I don't have a stand along o-scope.  My PSA P10 has a built in scope with fixed settings to measure it.  Here is a random graph:

Carlsbad2 - thanks for the graph. I’ve looked at my waveform and it’s clipped at the peaks and some junk on the wave too .  I’m really looking to see how well my power conditioner works. If we can agree that street power and house loads make it worse, but well designed gear will handle it, what was the reason you’re regenerating your power? Your PSA was an expensive investment?

OP: 

OP stands for "Original Poster" or the person who started this thread.

It's a good idea to tag those you reply to so they are aware. 

Shame on everyone discouraging you from experimenting.  Shame!  We need more hobbyist and tinkerers, not fewer, and we need more of them to have first hand knowledge of home power noise.  It also doesn't matter WHY the OP wants to tinker.  I remember many years ago I was thinking about making my own power regenerator.  It was a fun project and I would have learned a lot.  I went into an EE forum asking for help and one member immediately pulled out some thread I had typed in an audio forum to basically say no one should help me. 

Here we are now in an audiphile forum and I can't believe the number of opinions discouraging the OP.  I'm really disappointed in those of you doing so. Maybe this is just a learning experiment for the OP, and that's all it has to be.

Here is an article on doing so with a scope and an interesting thread from Stack Exchange and another from DIYaudio.