For water, that is. Of course you can argue that the Earth IS a closed system and anywhere you have ice, water and steam, you have a triple point. But no, it has to be that precise T-P definition from where you define the Kelvin (273.16 K and 611.657 pascals.)
The Earth is not a closed system at all; we keep losing stuff and getting other stuff from the rest of the universe. You can find points in nature which happen to be at triple-point conditions, it’s not as if those T and P conditions are particularly extreme; some of them may be closed within experimental timescales (a pocket of rock for example).
The required pressure is less then a tenth of a PSI so I doubt there is any natural occurrence. That’s that thing that nature abhors.
Dennis
Curriously, the required pressure (0.00603659 atm) is almost the same as the pressure on Mars (0.00628 atm). However, that’s just the nominal one at “sea” level; other parts of the planet will have different pressures. So I’d expect that at various times, there are places on Mars with the required temp and pressure. Whether there’s anything like pure water there is unlikely, though.
If you remove the 611.657 pascals restriction, which is merely the artifact left over from producing empirical units of measure that directly correlated to legacy arbitrary units the Earth and water would qualify.
If you take the stated approach you will need to go shopping around and the above Mars reference will work for a loose definition of closed systems.
Wait, how do you remove the pressure restriction? That’s the only pressure at which you can have water at its triple point.
Yep strike that claim as my memory failed me.
I forgot that Göttingen work on the other triple points related to it’s other phases.
Thanks for catching that.
I think the pressure is the partial pressure as opposed to the total pressure. It is entirely possible for a cave filled with just the right amount of air or natural gas to get to the triple point provided the temperature goes low enough. Maybe a cave near the poles ?
I don’t think so. If that were the case, room-temperature water would boil when exposed to air with zero humidity.
I think am77494 is right, though it’s been decades since i learned this stuff.
For example, here we have
Note: the vapor pressure is 600 pascals, not the total atmospheric pressure.
I’m just going to pedant up, and note that there’s more than one triple point of water.
Yeah, you get more than one triple point with polymorphs. The deal with water is that the other variant ices are even less likely to naturally appear at all on Earth, never mind at the triple point.
The familiar one is so well known and understood that it’s used to define the Kelvin temperature scale. I.e., 273.16 K is set to that temp. (And the corresponding points for Celsius and Fahrenheit.)
Back when I worked in a temperature metrology lab, we used triple point of water (TPW) cells as a reference temperature for our SPRTs. Used dry ice to form the mantle. Have good memories of those days. 
Ditto for me calibrating thermocouples in Thermo Lab in college Physics.
There should not be any “atmosphere” in a triple-point cell; they are sealed so that there is nothing in there but very pure water of a known isotopic composition. The three phases of water cannot coexist in equilibrium except at a unique pressure (and temperature).
It’s total pressure that matters, not partial pressure. Boiling is when you’re forming bubbles of vapor within the liquid. That won’t happen if the partial pressure within the bubble is less than the ambient pressure.
Exactly the TP standard depends on flat interfaces and a lack of the surface tension in typical air to be accurate.
Not that those conditions are easy to obtain if you look close enough.
My misguided earlier post was in relation to one non-reference case where this happens in a way that is close to meeting the OP’s requirements.
Snow melting in say the spring typically has quite similar conditions where a significant percentage of the melt is directly to vapor and another is liquid. This is not a perfect match with the stated requirements but is very common.
Evaporation is not the same thing as boiling.
Assuming you are responding to me, I was not referencing evaporation but sublimation.
Despite typically requiring 700% of the energy required to boil the water. In cold and dry locations ~20% to 41% of the yearly snowpack is lost due to sublimation and those losses often surpass the losses from wind drifting.
As snow has a high insulation capacity in dry sunny conditions it is not un-common for upper layers to have enough energy for sublimation while very close but lower layers melt into liquid water. Often that melt water lacks the latent energy required to produce significant amounts of evaporation. Sublimation is just a far larger energy sink.
This is extremely all dependent on multiple factors obviously.