I think it may be taking things a bit far to refer to heavy water as "chemically the same" as normal water - chemically indistinguishable might be a better phrase.
Heavy Water is a compound of an isotope of hydrogen called deuterium(D) combined with oxygen. Deuterium has an atomic mass of 2, as against 1 for normal hydrogen (H) due to presence of an extra neutron in the nucleus. The formula of heavy water is therefore D2O as opposed to H2O for normal water.
Because of these differences, heavy water should not be referred to as "chemically the same as normal water". The only similarities are between the chemical properties of the two compounds.
We do indeed drink heavy water each day as it is what you might call an impurity in conventional water.
However, it is incorrect to state that heavy water is "much denser" than conventional water. At 25 degrees C, heavy water has a density of 1.1056 grams per millilitre as opposed to 0.9982 for conventional water.
This means that in practice, if you poured heavy water into one tumbler and conventional water into another, no-one would be able to tell which tumbler contained the heavy water. On an industrial scale, it would also be very difficult to detect the difference in density unless one was looking for it with specialised equipment.
We've got a chemistry lecturer here at uni who's enjoyed baffling students for many years by freezing heavy water into cubes and dropping them into a glass of ordinary water. The cubes sink like a brick.
Heavy water boils at 101.42 degrees C and melts at 3.81 degrees C. It is also very slightly more alkaline than neutral conventional water.