In the sentence (IP)
The book, I think that I gave you
in which the object (complement of the verb of the CP "that I gave you") is fronted, is this fronted object the specifier of the whole IP? If not is there a specifier in this IP?
The topicalised object the book which is fronted (moved) cannot land in a theta-position. It'll violate Visibility Condition on Chains. Remember this is a non-trivial A-chain, it must have one theta role and one case to be visible. Spec,IP of this sentence is a theta-position occupied by the subject I.
The only option remaining is a theta-bar position. Spec,CP is a nice candidate. From this position, it'll have scope (being a topic) over the clause without affecting theta/case properties:
[CP the book C' C ∅ [IP I I' I [VP V' V think [CP that I gave you t ]]]]
It's similar to:
The book that I think that I gave you.
The picture differs in pro-drop languages. Spec,IP is taken to be a theta-bar position even in active voices (Spanish, Italian, Arabic, etc.).
