Army Man
George Meyer, right before he started working on The Simpsons in 1990, published a zine called Army Man. Several its writers became core Simspons writers, and it was the first place to publish Jack Handey's Deep Thoughts. The link above contains several quotes; here's an image of an actual page.
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Just a quick note of correction. I'm almost certain that National Lampoon published Jack Handey's "Deep Thoughts" before Army Man did. Now that I'm done getting my comedy geek on, I have nothing more to add.