Tb2Ti2O7 is a pyrochlore antiferromagnet that has previously been viewed as a spin liquid. This description fails to describe key features of its physics and more recently the concept of a quantum spin ice has been proposed as a better description. This is a spin ice subject to both thermal and quantum fluctuations. While this is a more apposite description of the physics it has not been verified experimentally. Earlier this year a prediction was made that a magnetization plateau would be observed along the [111] axis at low-temperatures in fields less than 1kG, with a level crossing at its upper boundary. Because of the low temperature required it is very difficult to verify this prediction. We propose to do longitudinal field muSR to test for both the magnetization plateau and the level crossing.