Is there a least reactive chemical species?
I think a good argument can be made for either helium or neon, the most noble of the noble gasses. Those are the two prototypical unreactive elements. They are the only two stable elements for which no more complex compounds (i.e., other than the single atoms themselves) have yet been isolated, at any temperature. The slightly more reactive element argon will admit formation of compounds such as argon hydrofluoride ($\ce{HArF}$). This compound is only stable up to $\mathrm{17\ K}$, because any hotter and the frail bonds are overcome by random thermal collisions which break the compound apart into $\ce{Ar}$ and $\ce{HF}$.

Picking which of helium or neon is less reactive is a bit more difficult. A naive analysis of periodic trends would point to helium as the most inert, but more detailed computational studies suggest that at least in some cases neon may be less reactive. For example, the extremely Lewis acidic compound beryllium monoxide ($\ce{BeO}$) may potentially form an isolable, if very weakly bound, compound with helium, $\ce{HeBeO}$, but neon is not thought to form the analogous $\ce{NeBeO}$. $\ce{HHeF}$ may also be just barely stable, whereas $\ce{HNeF}$ is not thought to form. None of these have yet been observed in the laboratory, but there is definitely ongoing research into coaxing helium and neon to make isolable compounds.

All that said, we can get helium and neon to react, if we drop the requirement that the product must be isolated (that is, "put into a bottle"). Chemical species such as $\ce{He2^+}$, $\ce{Ne2^+}$ and $\ce{HeNe^+}$ have long been known from mass spectrometry experiments, they just can't be isolated because that would require the presence of a counterbalancing negative ion, which would immediately proceed to react with the positive ion and cause decomposition with release of the noble gas. You can also bring what is arguably the most reactive species in chemistry, the hydrogen cation ($\ce{H^+}$) into the fray. Helium and neon will both easily react with $\ce{H^+}$ to form $\ce{HeH+}$ and $\ce{NeH+}$ , as shown by the exothermic proton affinities of $\ce{He}$ and $\ce{Ne}$. Again, these composite particles cannot be isolated, as they are amongst the strongest Brønsted-Lowry acids in existence, and will protonate anything they come into contact with in order to release the neutral noble gas atom. Some other possible non-isolable relevant noble gas ions are $\ce{FHeO^{-}}$, $\ce{HeCCH+}$ and $\ce{PbHe15^{2+}}$ (!), among others.

Edit: I forgot to mention that there are a few other cases of helium or neon binding to other atoms. By exciting one of the electrons in the atom, it is possible to coax it to bond with another one, forming an excimer or exciplex. See for example, the dihelium excimer $\mathrm{He_2^{*}}$. This is a short-lived species that still can't be isolated, however, because in a matter of microseconds it releases a photon and de-excites, promptly separating into the two free atoms.