Tim,
Do you have a paperclip holder next to your monitor on the right side of your monitor? (No one thinks about the tiny magnets they have inside.) Also is there anything under the desk as in a drawer just under the monitor? (Even the older style Telephones had magnets in them.) You could try moving the location of the monitor just to be sure it is not some sort of outside influence causing it.
If it is not magnetic, and it is not a Degauss issue (as Lost_luggage34 mentioned) then try the monitor on another computer and visa versa to see if you can repeat the problem.
Take Care,
Richard