Yes and no. Chlorine will not harm a diamond, but it can eat away at gold and silver. One soak, however, wil be fine. As long as you rinse off the ring in some jewelry cleaner. If your ring is platinum, don't worry at all.
Chlorine may damage white gold. It can corrode away the nickel it's alloyed with. Even if the damage is invisible, it may weaken the prongs that hold diamonds on. This is likeliest with a white gold piece, but have any chlorine-exposed jewelry checked.
Yes, chlorine can damage the diamond ring, because it is a harsh chemical. Chlornine reacts with diamond make it corrode and brittle and fade away the look. Swimming pool water, tap water contains chlorine, hence avoid diamond rings come in contact with diamond rings.
What you should really be concerned about is the mounting of the ring. Exposure to chlorine doesn't damage diamonds, but Chlorine will eat away or discolor certain kinds of metal. Platinum is safer from it than most metals, but don't wear your ring in any swimming pools if it's made of white gold, gold, or silver.
YES, CHLORINE CAN DAMAGE THE RING AS IT IS A TOXIC CHEMICAL AND MORE EXPOSURE TO CHLORINE LEADS TO CHIPPING OFF ELEMENTS, COLOUR OF THE RING GETTING FADED SPECIALLY IN SWIMMING POOLS.SOME PEOPLE THINK THAT IT CAN BE USED AS A CLEANSER FOR JEWELLERY.