Pressure on the chest can be caused by heart problems.
However, you don't give us information about your age, sex, occupation, family history, habits, how long the pain lasts, what brings it on, what eases the pain, whether it occurs at night, whether movement affects it, whether eating affects it, etc etc. On page 18 of my book for the laity on Chest Pain When and When Not to Worry (Pelican Publisher, Gretna, LA)I discuss the descriptive language of chest pain - which is pertinent to your question.
To speculate on "what this could be" would be a mistake.
I suggest you consult a doctor about this symptom and be prepared to provide much more information.
Please be aware that I am unable to diagnose medical conditions online.