True
Cells are always functioning, and their functions are carried out by proteins. But like all molecules, proteins will break down and must be replaced. The process of producing proteins involves gene transcription. Therefore, gene transcription is constantly occurring.
Now, in support of my colleagues above, not every gene in a cell is constantly being transcribed. In fact, many genes in a cell may never be transcribed! It all depends on the function of the cell. For example, most human cells do not produce insulin, so they don't need to produce the enzymes needed for the production of insulin. They still have the genes for those enzymes, but they are never transcribed. Also, during mitosis, no genes are being transcribed, but genes in other cells are.
I guess it all depends on how you interpret the question.