I'm no MD, but when I first started cardio I my chest would get tight also. However, for me the reason was simple: The diaphragm is a muscle! Wiki. And, it should be trained like any other muscle. Slow and steady at first, trying to run too fast too soon (soon as in inexperience or too soon into any particle jog/run) will fatigue the diaphragm and wear the runner out prematurely. Once I slowed down, and took my time, the tightness would come back after so long, but I could tell my lungs were getting stronger. (hint, that's why products like this are on the market).
As far as the mental goes, It's one of those things (for me at least) when the body starts to fatigue, mental narration sets in and says it's time to quit. How hard you fight that voice is up to you, and it's that fight that separates a mediocre day in the gym from an awesome one.
I would try running on a regular basis if I were you, to see if it goes away. Remember to only change one variable at a time: So, for example, if you're increasing running frequency, don't increase duration or intensity. To build on that example: If you start running 3 times a week instead of one (frequency), don't try to run farther or longer than usual (duration), or increase your distance in any given time (intensity). Stick to one or the other, either a set amount of time, or a set distance. If the tightness continues after a few weeks, and your cardio endurance isn't increasing, there may be something else going on.
Final thoughts: Make sure you eat halfway decent also, since this isn't a diet q&a site I have to refer you to other corners of the 'net, until the nutrition site is up.
Consult a physician before participating in any exercise regimen.