John Glenn February 20th 1962 Friendship 7
John Glenn was the first American to Orbit Earth , he wore a Tag Heuer Stop Watch which had been modified with elastic bands so that it would fit over the spacesuit.
This Heuer stopwatch served as a “backup clock” for the timing instruments aboard Friendship 7 and was started manually by Glenn 20 seconds into the flight.
It is currently on display at the San Diego Air and Space Museum
So Tag Heuer became the first Swiss watch to be used in space.
You can read more about this on the Tag Heuer site.