Experimental cancer drugs may also help to prevent the development of a common cause of heart failure.
Drug may have multiple uses
Cardiac hypertrophy - the enlargement of the heart muscle cells - can be fatal.
Tests on animals by researchers from the University of Pennsylvania showed the cell enlargement could be blocked by using HDAC inhibitors.
The study is published in the Journal of Clinical Investigation.
Cardiac hypertrophy can be a perfectly healthy response to exercise and training - heart cells grow larger like any other well-conditioned muscle.
However, it can be result of an unhealthy cardiovascular system, or a genetic defect, in which case it can be dangerous.
This is because the cardiovascular system has to work harder to push blood through the heart as the enlarged tissues reduce the space through which it must pass.
Lead researcher Professor Jonathan Epstein said: "Despite the fact that this is a common everyday problem for clinicians and patients, we have very few, if any, medications that are directed at halting the cellular events responsible for this deterioration.
"These HDAC inhibitors may be among the first known medications to prevent cardiac hypertrophy."
The new research is based on the theory that some cases of hypertrophy are caused by over-production of a protein called Hop.
Hop is thought to control heart cell growth. It is abundant in foetuses and newborn babies, but not normally in adults.
However, it seems that some people have higher than normal levels of the protein, and this may lead to increased growth of the heart muscle cells.
The researchers believe the DHAC inhibitors work by blocking the chain of chemical reactions which ultimately triggers renewed cell growth.
Professor Jeremy Pearson, associate medical director of the British Heart Foundation, said: "This is an intriguing study providing new insights into the molecular mechanisms that can lead to cardiac hypertrophy.
"The suggestion that HDAC inhibitors may be useful to treat cardiac hypertrophy is tantalising.
"However, before they could be tested in humans more experimental work needs to be done to determine whether these drugs consistently reduce cardiac hypertrophy, which is the heart's response to a wide variety of different events, and to ensure that they do not have unrelated side effects."