The largest satellite in the solar system with a substantial atmosphere is Titan, a moon of Saturn.

Here's why:

* Largest: Titan is the largest moon of Saturn and the second largest in the solar system (after Jupiter's Ganymede).

* Substantial Atmosphere: Titan has a dense atmosphere composed mainly of nitrogen, with methane and other hydrocarbons. Its atmospheric pressure is actually higher than Earth's.

While other moons like Ganymede and Europa may have thin atmospheres, Titan's is the most significant and well-developed, making it unique in the solar system.