Bring a pan of salted water to the boil. With an oyster knife, open the oysters and scoop the oysters' flesh out of the shell. Cut them in half and put them back in their own water, taking care not to leave any bits of shell in the oyster water.
Gently melt the butter in a large saucepan.
Meanwhile, add the pasta to the pan of boiling salted water. It should take two minutes to cook, if you're using fresh pasta, or according to packet instructions. Drain the cooked pasta, reserving some of the cooking water.
Add the drained pasta to the pan with melted butter. Then add the oysters and the oyster water. Add the chives, vinegar and lemon. Stir for a couple of minutes, just to warm the oysters up. Add more water or butter if needed.
Serve immediately.
