Generative AI assistants are becoming an advertising medium, embedding sponsored content in their answers. This setting departs from classical position auctions in two ways: an ad's click-through rate depends on the passage that hosts it, and because users stop at their first click, earlier ads take clicks from later ones. This competition for clicks makes truthfulness delicate: a higher bid can reshape the allocation and put a competitor ahead of the bidder, reducing the bidder's clicks. Existing mechanisms either attain a constant fraction of the optimal welfare (advertisers' total click value) but are not known to be truthful, or are truthful but their welfare guarantee degrades as the number of passages grows. We achieve both even when the answer and its editorial order are fixed before bidding. Assuming each ad's click-through rate when reached is known and unaffected by omitting other ads, we give a computationally efficient mechanism that is truthful in expectation and attains at least half the optimal welfare under free reordering. Our key idea, click thinning, omits ads at random, showing earlier ads less often so that each ad's overall click probability no longer depends on the order of the ads. Welfare maximization then reduces to a tractable matching problem, and solving it exactly with VCG-style payments makes truthful bidding optimal in expectation. Characterizing the click probabilities that omission can achieve sharpens the approximation factor from $2$ to $2-(1-δ)^{K-1}$ when at most $K$ ads are shown and each click-through rate is at most $δ$. This factor is the best possible for any order-preserving rule, even one that ignores incentives and computation, so truthfulness and computational efficiency incur no additional worst-case loss.

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