In their memoirs, Nikita Khrushchev and Vyacheslav Molotov both claimed that Lavrentiy Beria, the longtime of the Soviet secret police, boasted that he had killed Stalin in March 1953. Nikolai Vlasik, Stalin's personal bodyguard, also thought that Beria had something to do with Stalin'a death. Now let us ask ourselves two questions before we proceed.

The first question is: Did Beria have the means to kill Stalin? The answer is yes: he almost certainly poisoned Nestor Lakoba back in 1936, possibly offered to poison Sergo Ordzhonikidze, and was a general expert in arranging deaths to make them plausibly look like accidents.

The second question is: Did Beria have reason to want to kill Stalin. The answer, again, is yes. After World War II, Stalin has grown suspicious of his inner circle. He did not like or trust Beria any longer and desperately wanted to find a way to get rid of his longtime associates, Vyacheslav Molotov and Anastas Mikoyan. There were also signs that, by the early 1950s, Stalin might have been suffering from dementia. The so-called Doctors' Plot and Stalin's general campaigns against Jews were so bizarre that even much of his inner circle thought that he was losing it. Georgy Malenkov and Beria were also worried about the increasingly unstable Stalin's access to nuclear weapons, as neither were especially thrilled about the idea of nuclear holocaust.

It's also worth mentioning that, after the beginning of the 1930s, Stalin's inner circle were the group that stood the best chance of successfully assassinating him, despite the fabricated assassination plots supposedly orchestrated by his political enemies, Leon Trotsky, Grigori Zinoviev, Lev Kamenev, Nikolai Bukharin, Aleksey Rykov, and others, during the Great Terror.

However! Beria having the means to poison Stalin and the reason to want to do so are not ironclad proof that he actually did. When Beria was arrested and judged with various crimes (some of which he committed and some that he didn't), the subject of him murdering Stalin wasn't brought up.

Stalin appears to have died of a stroke caused by a combination of high blood pressure, Atherosclerosis, and a stomach ulcer. This rules out death by most common poisons, but poisoning by the anticoagulant warfarin is still possible.

However, it is virtually undisputed that Beria, Khrushchev, and Malenkov took their sweet time before summoning a doctor when they found that Stalin had collapsed from a stroke. Whether or not a doctor could have actually done anything to help is unknown, but it's still unusual and especially because the three then went out of their way to make it seem like they'd immediately summoned a doctor rather than delaying.