Thermochemistry - zero heat energy
You could just as well have wondered is there any number which is neither negative nor positive. Yes, there is such number, and it is called zero. It is rarely encountered among the real-life physical values, though, unless enforced by some law (which is not the case here). After all, there are immensely many positive numbers, and equally many negative numbers, and only one zero. You can hardly expect to hit it by choosing numbers at random.

Then again, reaction enthalpies are subject to variation with temperature, so if we pick any reaction with low enthalpy, it is quite probable that there is a certain temperature at which the said enthalpy is exactly 0. That would be the answer to your question. It is for entropy to decide whether the reaction will occur spontaneously at this temperature. Chances are it will.

On a side note, there is a huge number of "void reactions" like $\ce{H2 + H -&gt; H + H2}$ with guaranteed zero enthalpy at any temperature, but many would object against calling these things reactions in the first place.

So it goes.