The sentence is expressing a hypothetical situation in the past, the correct answer is had had, as it is the past perfect form of the verb "to have" that is used for the third conditional sentence. The third conditional sentence is used to talk about a hypothetical past situation and its result in the past.
Conditional Sentence
As is typical for many languages, full conditional sentences in English consist of a condition clause or protasis specifying a condition or hypothesis, and a consequence clause or apodosis specifying what follows from that condition. The condition clause is a dependent clause, most commonly headed by the conjunction if, while the consequence is contained in the main clause of the sentence. Either clause may appear first.
Different types of conditional sentences (depending largely on whether they refer to a past, present or future time frame) require the use of particular verb forms (tenses and moods) to express the condition and the consequence. In English language teaching the most common patterns are referred to as first conditional, second conditional and third conditional; there is also a zero conditional and mixed conditional.