Is this technologically feasible?
What is the oldest unmaintained working man-made mechanism? I have no idea, but I'd hazard that it's closer to 100 years old than 1000. Things that do keep working do so because they're regularly maintained by people. I'm thinking of stuff like multi hundred year old mechanical clocks.
Assuming you mean some kind of electronics made with transistors, you would have to deal with unsolved problems including
* how you build a billion-year power source
* how you deal with transistor aging on the billion year timescale
* how you deal with medium & large scale events over a billion years (example: weather if on a planet, micrometeorite impacts if in space)
Heck even the clock of the long now <https://en.wikipedia.org/wiki/Clock_of_the_Long_Now>, a clock that works on a scale of 10k years, is a major engineering challenge that will most likely be unsuccessful (my opinion)
Technologically feasible? Probably and likely