"I thought so," cried the cook; "this here is a p'inter. Right up there is our line for the Pole Star and the jolly dollars. But, by thunder! If it don't make me cold inside to think of Flint. This is one of HIS jokes, and no mistake. Him and these six was alone here; he killed 'em, every man; and this one he hauled here and laid down by compass, shiver my timbers! They're long bones, and the hair's been yellow. Aye, that would be Allardyce. You mind Allardyce, Tom Morgan?"
At least one source says it is an expression of surprise. Timbers were the largest main support beams for the decks and ribs of a sailing ship. Only violent movements, such as heavy seas or a collision, could cause them to shake (or shiver). This term came to be used for any deed or action that was deeply surprising to a sailor or caused great fear. I guess a landlubber's equivalent would be an event that would send "chills down one's spine" (the spine being the main support of the human body)