kT is very little energy compared to a chemical bond. Take for example [0], they give an excitation energy for water of about 8 electron Volts which is ~750 kJ/mol, whereas kT at room temp is about 2.5 kJ/mol.

[0] http://scitation.aip.org/content/aip/journal/jcp/128/10/10.1...

Right, but it's the 'every once in a while" part that I wonder about, i.e. the variance of that distribution. Maybe you could argue that since the Maxwell-Boltzmann distribution is narrower the lower its mean, if kT is small then it's an exponentially tiny effect.

So yes, kT is small on average (does fluctuate) and it is also 1 kT per degree of freedom. So yes, in principle a few hundreds of atoms could randomly fluctuate in energy to create this effect. However, this is hyper unlikely. I would be suprisd if it happened once in the life time of the universe. Also consider that you cannot create Maxwell demons[1].

[1] https://en.m.wikipedia.org/wiki/Maxwell%27s_demon