No, chest X-rays and any other type of X-ray are safe for someone with a stent or any metal containing object in the body or head. Its also safe to have a CT scan if you need one.
The concern about metal moving during an imaging procedure relates to MRI (magnetic resonance imaging). The strong magnets used during an MRI can move some metal objects inside the body.
Its also safe for most people with metal heart stents to have an MRI, especially if it was implanted more than 6 weeks before the test. Just let the MRI technician know what type of stent you have. He or she can look up the MRI safety for your type of stent.
Always tell your doctor about any metal objects that might have been implanted or in your body, either surgically or accidentally. For example, is there any chance that metal fragments ever got into your eye?