Much of the support for and evidence against the Big Bang comes from physics. However, there is some chemistry involved. The most compelling chemical evidence for the the Big Bang is the variety of elements that are observed to make up distant galaxies, and the relative amounts of these elements.
Astronomers can detect the elements of distant galaxies and stars through spectroscopy. Elements, when heated, give off characteristic spectral lines of specific colors when viewed through a prism. When the light coming from distant galaxies and stars is broken down into its various wavelengths the spectra of specific elements can be seen, and the brightness of these lines corresponds to the relative abundance of elements. The relative abundance of elements observed in this way in distant objects corresponds to that predicted by the Big Bang theory.
Some of the younger bodies in the universe, such as our sun, don't show the relative amounts of elements of older objects because they are much younger that the universe and have a different composition than older stars. While this seems to refute the Big Bang theory, there's an explanation that justifies the observation.
Thermodynamics arguments are often used to refute the Big Bang. Thermodynamics is a branch of chemistry and physics that deals with energy changes in chemical reactions. The First Law of thermodynamics states energy can't be created or destroyed. The Second Law of thermodynamics states that systems become less organized or more random over time. The Big Bang would appear to violate both laws, as a large amount of energy was produced and matter was formed out of seemingly nothing, resulting in more order. One must remember that the Big Bang theory attempts to describe the development of the universe over time, not the origin.