[from where the red fern grows] In the first chapter, what causes the narrator of the story to remember his childhood?

The hound he saves.

Explanation:

When the narrator saves the hound, he determines that is a hunting hound, much like the two he had growing up, Old Dan and Little Ann, which were Redbone Coonhounds. This is further proved when his mind wanders and he thinks about where the dog could be from, possibly the Ozark Mountains, where he once lived. This is once again backed up when he makes the following statement that "Although the old hound had no way of knowing it, he had stirred memories, and  what priceless treasures they were."

in our power to make a world happy - to teach mankind the art of being so - to a character hitherto unknown - and to have, as it were, a new creation intrusted to our hands, are honors that command reflection, and can neither be too highly estimated,