Ajewelry company has announced that they have created gold from reacting copper and carbon in a chemical process. according to dalton's atomic theory, is this possible?

No John Dalton made a fairly fundamental description of an atomic theory that still holds today for chemistry. In his theory, there are 4 things to consider 1. All matter is made of atoms, and atoms are indivisible and indestructible. * This right there makes the process described in the question impossible since the described process would require the destruction of copper and carbon, which is in violation of the first element of Dalton's theory. 2. All atoms of a given element are identical in mass and properties. 3. Compounds are formed by a combination of two or more different kinds of atoms. 4. A chemical reaction is a rearrangement of atoms. * This also is in conflict with the process described in the question. Since the process is described as chemical, that eliminates nuclear methods just as fission, or fusion. Now the spirit of the theory remains true, but modern knowledge does make the details different. For instance, we know of isotopes, so #2 isn't strictly true any longer. We also know of nuclear reactions so #1 isn't completely true either. But in general, his theory is as useful today as it was two hundred years ago.

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