I realize the Aztecs and the Native Americans mentioned here are not
exactly paleo. Not sure how much of this is marketing hype, but this story
about chia seeds suggests that running long distances was common.

http://newtimes-slo.com/archives/cov_stories_1999/cov_072299.html

Little is known, however, of the seeds’ tremendous nutritional value and
medicinal properties. For centuries this tiny little seed was used as a
staple food by the Indians of the Southwest and Mexico. Known as the
"running food," its use as a high-energy endurance food has been recorded
as far back as the ancient Aztecs.

It was said the Aztec warriors subsisted on the chia seed during their
conquests. The Indians of the Southwest would eat as little as a
teaspoonful when going on a 24-hour forced march. Indians running from the
Colorado River to the California coast to trade turquoise for seashells
would only bring the chia seed for their nourishment.