At last Tuesday's Club meeting young master Andrew Lee asked if I knew when they first started timing chess games. (Andrew has yet to develop an appreciation for time controls longer than game 10; and prefers game 7.)
Among my favorite chess books is Irving Chernev's Wonders and Curiosities of Chess; published by Dover in 1974. On page 130, Chernev reports:
"The first match in which the players were restricted to a certain number of moves per hour was the one between Anderssen and Kolisch in 1861. An hour glass was used, and each player had to make 24 moves in two hours."
I have seen pictures of these hour glasses which were inclosed in a cage that pivoted in the center in order to be turned horizontally when it was not your turn to move. This of course required a device be used for each player.
Andrew, I hope this answers your question.
For more info, see also:
History of Timers and Clocks in Chess Matches