As a cosmetic scientist in the making having just studied the structure of hair, removal and cleansing, I can confirm that it is a myth. If you look at the structure of hair closely, the tip is very fine/tapered and the centre and root are much thicker. Cutting the hair acts like cutting the end of a rope; the threads or fibres (or layers of cells, as they are on hair) fray at the end, appearing thicker. This effect is increased if moisture is lost from the hair (such as from heat damage), causing more obvious split ends. If the hair was allowed to grow back after plucking (or waxing) cleanly, however, the tip is still tapered rather than split.
A less sciency description:
http://www.sciencealert.com/does-hair-really-grow-back-thicker-and-darker-after-shavingOP, as someone suggested earlier, it does sound like you may have a hormone inbalance. A doctor may be able to put you on the pill or something similar to balance them out a little. Overgrowth is especially likely if you are going through puberty, the effects of which can continue into adulthood for some people. Have you spoken to any relatives about it? Do they have a similar problem? Is it only your chest that concerns you or is there growth elsewhere?
Methods-wise, definitely avoid shaving. Cutting the hair will give a coarser appearance, so try and use a cream or wax so as not to leave blunt ends. If it's a small area that concerns you, perhaps consider plucking the excess? It will be a slow process, but means that because you aren't removing all the hair at once, it won't all grow back at once, so it will appear more sparse as opposed to being completely gone, but won't leave you with stubble or an even regrowth. Anything that removes all hair at once means it will all grow back at once, and might not be long enough for the wax to catch it until it's more visible. Only try these if hormonal investigations don't help. Good luck, whatever you do