The answer is an envelope. It contains a letter.
There is no one-word 8-letter palindrome in English, apparently!
strength
Hint is't an 8 letter word.... FB game
One option is the word bouffant.
Multiple
Not that I know of, but my dad had a close one, 7 letter word, negated.
Armchair is an 8 letter word. The 7th letter is i.
Unsorted is an 8 letter word meaning uncategorized. Mishmash might also be one, but I'm not sure it's a real word.
An 8 letter word, with just one letter in it, is ENVELOPE. 8 letters in the word, 1 letter inside the envelope.
strength
One is shutting.
pleasenow