Let C be the subgroup of all diagonal matrices in SL(n,Q _p). In the first part of this paper we study and give a classification of the Chabauty limits of SL(n,Q _p)-conjugates of C using the action of SL(n,Q _p) on its associated Bruhat–Tits building. Along the way we construct an explicit homeomorphism between the Chabauty compactification in sl(n,Q _p) of SL(n,Q _p)-conjugates of the p-adic Lie algebra of C and the Chabauty compactification of SL(n,Q _p)-conjugates of C. In the second part of the paper we compute all of the Chabauty limits for n≤4 (up to conjugacy). In contrast, for n≥7 we prove there are infinitely many SL(n,Q _p)-nonconjugate Chabauty limits.