I added a chandelier in a dining room between 2 can lights.I tapped off of the can lights with 14/2 romex to the chandelier. The can lights were ran in 12/2 and the circuit is on a 20 amp breaker. I believe this is against code, should I be worried that the 14/2 could overheat and cause a fire???? Because I'm a bit worried that this could be a real issue.

Being an Australian, I'm no expert on the NEC, but I'll give my 2 cents anyway:

Technically, 14/2 can probably handle 20A under ideal conditions (free air, not surrounded by thermal insulation, not bundled with other cables). The question, then, is what conditions you've installed it in (i.e. how far will it have to be de-rated). I'm not that familiar with the "official" ratings, however, so I'll leave other members experienced with the NEC to answer with them.

In all likelihood, what you've set up will work fine, as long as that chandelier is within the rating of the 14/2. But I'm not one who likes to take reasonably avoidable risks - however small - and I'm quite sure others here would agree. If I was doing this, I would have used the 12/2 unless I was really strapped for cash; if mainly to be consistent with the rest of the circuit (preventing any future confusion).

From a practical sense it is not particularly dangerous since this is a fixed load assuming we are not talking about a ball room luminaire with 1000 bulbs in it but it is still a code violation.

Is there a tap rule?

A #14 wire is fine with 20 amps but the termination point will overheat. This happens on a 3 wire circuit when the hots are the same phase. The neutral bar gets hot and everything near the overloaded termination gets crispy. Because you ran a tap, it will be okay; and, the 20 amp breaker probably isn't loaded to 20 amps.

Note that the tap rules are in the over current article. A 14ga tap on a 20a circuit would still need 15a Over current protection somewhere. As close as you get is fixture wires but that needs to be within the listed equipment.

For the Canadians who read this, we have a tap rule (30-412) that allows a 7.5m (24.5 foot) tap with a #14 from a 20 amp circuit, for one light or one row of lights provided #14 is large enough for the load. So, it is safe in the North but not in the South.

I agree with what Greg said a few comments up. Yes, it more than likely will be 'ok' dependent on the load of the fixture(s). But, it is a violation as the NEC regardless.

Now, does this happen? Likely yes. Have I red tagged this scenario? I would IF I came upon it.