Chlorophyll is organic, not living, which is a fancy way of saying that it contains carbon. As for your question about boiling, it depends on whether or not the heat from boiling will disrupt the chemical bonds and destroy the molecule. According to Wikipedia, chlorophyll a will melt at around 117°C (I'll assume that chlorophyll b is similar), which is higher than the boiling point of water, so if the temperature is strictly maintained, the chemical should stay intact.