Jacob's solution works but there are some additional alternatives. You could put the xrandr commands in your .xsessionrc file, so that they're executed at startup. You could also just write an xorg.conf entry to set your monitors explicitly left/right of each other. I'm not at my PC so I'm regrettably short on details at the moment, but will come back to fill them in later if I get time. In the meantime it would be worthwhile for you to read up on both xrandr and xorg.conf files in general; you might discover a better solution than what I end up putting here anyway. ^_^
EDIT: OK I'm finally getting around to this.
Using xrandr and ~/.xsessionrc
The xrandr utility is used to both get and set information about your displays. Type xrandr by itself on the command line and you'll get a listing of all your displays and the "modes" that they support. Here is some example output corresponding to an old Dell 4:3 LCD.
DP2 connected 1280x1024+1920+0 (normal left inverted right x axis y axis) 338mm x 270mm
   1280x1024      60.0*+   75.0  
   1152x864       75.0  
   1024x768       75.1     60.0  
   800x600        75.0     60.3  
   640x480        75.0     60.0  
   720x400        70.1  
You would add modes to these if your monitor's resolution isn't right, etc., but your problem is about positioning. xrandr provides simple parameters --left-of <output> and --right-of <output> that allow you to dictate where your displays sit in relation to each other.
So let's say your displays identify as FOO1 and FOO2. (They never will; this is just an example.) If you want FOO1 to be always on the left of FOO2, you would enter:
xrandr --output FOO1 --left-of FOO2
or
xrandr --output FOO2 --right-of FOO1
Typing this on the command line will immediately make the change for your current session. Inserting the same line into your ~/.xsessionrc file will make the change effective every time you start X.
Using xorg.conf
Your other alternative is to write an xorg.conf entry that will dictate display configuration as part of the X startup process. If you're on Ubuntu then this will likely be part of a file in an xorg.conf.d directory, either at /usr/share/X11/xorg.conf.d or /etc/X11/xorg.conf.d. So if you don't already have one, create a config file to drive your display adapters and monitors. I called mine 01-monitors.conf to ensure it got executed first. Reusing the previous example with FOO1 being to the left of FOO2, we can set up the same preference here with a Monitor config section.
Section "Monitor"
    Identifier "FOO1"
    Option "LeftOf" "FOO2"
EndSection
Note that the Identifier is the same one you'd get from xrandr.
Further Reading
The man page for the xorg.conf configuration system is available at http://www.x.org/archive/X11R7.7/doc/man/man5/xorg.conf.5.xhtml