Is tripleaxis planet possible? Imagine. Our solar system. Our sun. Then earth and moon orbiting it. And you have "powers" to create any planet you want, any size, any density, any weight and any velocity. Would it be possible for you (using all knowledge of earth), to create a natural satellite to moon? Whose trajectory would be almost circular/ellipsoidal?
Question actually goes only as follows: Can moon of moon (actual moon) of moon (earth) of sun exist?
 A: This is possible. For example, this post provides a good explanation of the math involved.
The key point is whether an object lies in the planet's Hill sphere or the moon's Hill sphere:

Can the Moon have a moon?
Yes, the Moon could have a sub-satellite. If we look at a system of the Earth, Moon, and a sub-satellite, the same idea as above applies. The Moon has its own Hill sphere with a radius of 60,000 km (1/6th of the distance between the Earth and Moon) where a sub-satellite could exist. If an object lies outside the Moon's Hill sphere, it will orbit Earth instead of the Moon. The only problem is that the sub-satellite cannot stay in orbit around the Moon indefinitely because of tides.

As long as the gravitational attraction of a satellite is consistently stronger than the body the satellite orbits, a third body will orbit the satellite.
There are obviously limits to how small you can go with this, as gravity is a relatively weak force at small scales.  At some level, either the Hill sphere is smaller than the object itself or other forces dwarf gravity's impact. For example, a person's gravitational field is too weak to attract its own satelite; the Earth wins that one every time.
A: If things are in close, you have the three-body problem (four, given the sun - but it is distant).  Three-body orbits are not uncommon in the universe.  Orbit evolution prediction is fundamentally impossible, though abundant special solutions exist,
http://en.wikipedia.org/wiki/Three-body_problem 
http://news.sciencemag.org/physics/2013/03/physicists-discover-whopping-13-new-solutions-three-body-problem
