。
I thought she had no right to do such a thing.
Literal
She [topic-は] that-kind-of thing [object-を] do right [subject-が] not-exist [quotative-と] I [topic-は] thought.
An embedded clause inside ~と思った: the entire claim 'she has no right to do such a thing' is the content of the speaker's thought, marked with quotative と. 権利 (kenri) is the legal/political/social term for 'right, entitlement' — same word that gives 人権 ('human rights') and 権利を持つ ('have a right'). The clause-internal は on 彼女 and the matrix-clause は on 私 set up two parallel topics; this layered topicalization is one of the things that makes Japanese both compact and interpretively rich. ~する権利がない is the standard frame for 'have no right to do X.'