Where does the thermal energy come from in a chemical change when two substances react with one another?
The energy was in the chemicals, in the form of bonds. Energy is liberated when there is bond formation. As the reaction between $\ce{Cu}$ and $\ce{HNO3}$ is feasible at room temperature so it happened. 

And another thing, room temperature is a nice temperature for that reaction because first we need to break bonds of $\ce{HNO3}$ to make new bond, which is easily done at this temperature.

Now coming to your question, the answer is 'no'. The first law is still safe. You know it wrong. The truth is (from wikipedia) : "the total energy of an isolated system is constant; energy can be transformed from one form to another, but cannot be created or destroyed". 

Give special attention to the word 'total energy', you said the 'thermal energy' in your question. And the total energy (atleast in this case) is conserved in the form of summation of thermal energy and bond energy.