You should tell your father that he needs to seek immediate medical attention. Although there are many causes of tightness in the chest, including several that are not very serious, such as heartburn, in a male the age of your father, the possibility of trouble with the heart always needs to be ruled out. Other symptoms that would be concerning would be chest pain, shortness of breath, and sweating. Also, if the chest tightness comes on with exercise that is also concerning.
If your father cannot get in to see his doctor
right away, it would be appropriate for him to go to the emergency room for evaluation. Tests that are typically done to rule out a heart attack include an electrocardiogram, which is a simple electrical tracing of the heart. Also, it is common to take a few simple blood tests which can detect any damage to the heart muscle cells. If these tests check out as normal, his doctor may also want to do a stress test to uncover any additional symptoms.
Immediate medical evaluation is important, because waiting can result in permanent damage to the heart whereas if a heart attack is caught right away it is often possible to prevent this.