How to fix the WordPress prepended linebreaks error

A while ago I noticed that the RSS feed for MyPieceOfTheInter(.)net stopped working.  Strict XML parsers like those in Google Chrome and Internet Explorer refused to parse the RSS feed.  Looking around different places, I found that a lot of weirdness was happening.

Viewing the source of the homepage reveled that there were unexpected linebreaks at the top of the document.
wordpress line break error 1

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