It was 1959, two years after the USSR had launched Sputnik. The USSR was showing off its achievements to other countries. Most were uninteresting, at least to the US government (in a country with electricity, stealing models of power stations would've done little good), but one was quite interesting: the Lunik spacecraft. It had to be a model, the CIA figured. After all, the Soviets had to have known Americans would've looked at that and tried to steal it, or at least figure out how it was made. Models were safer. But American agents figured it wouldn't hurt to look, and they found that it was a real one, albeit with some critical parts, like the engine, removed.
But you can't just saunter in during the exhibition and steal it, for fairly obvious reasons. The key was that it was a traveling exhibition, and as it was being transported, via some maneuvering and some possible/probable kidnapping of truck drivers (Sydney W. Finer notes the truck driver was "escorted to a hotel room and kept there for the night" on page 36 of his article[1] on it), the CIA managed to gain access to it.
After getting the all-clear to start, and, at one point, being scared witless by a possible ambush (it was people lighting the lamps, as was regularly scheduled), they opened the box carefully and began taking photographs of it. They took photographs or made drawings of everything, taking small amounts of things for study. Then they put it all back together and, eventually, gave it back to the original driver. They did their job hiding it well. In 1967, according to Finer's article (final page), there was "no indication the Soviets ever discovered that the Lunik was borrowed for a night."
The CIA has now declassified some documents on it[2], referring to it, somewhat euphemistically, as a 'loan' or 'borrowing' rather than 'theft'.
[1]https://www.cia.gov/readingroom/docs/THE%20KIDNAPING%20OF%20...
[2] https://www.cia.gov/readingroom/collection/lunik-loan-space-...