That’s a tough question. I presume our evolutionary relatives the apes are the closest to us in intelligence, but you would have to ask an evolutionary biologist for a more detailed answer to that question.
My money is on chimps, which I have a particular fondness for and are pretty smart – can learn sign language, for example, and in the wild they make their own tools, such as using long sticks to poke grubs out from under bark.
They also get malaria, incidentally – some work I was involved with recently showed that up to 50% of chimps and gorillas are infected with malaria parasites!
There are mixed views on this. Chimpanzees are unsurprisingly highly intelligent, given how close they are to us, yet a dog can learn far more words than a chimp. I believe the world’s smartest dog knows more than 400 words (it’s a collie), and it’s impossible to get chimps to learn more than a few. Perhaps this just tells us that the tricky thing here is how we define intelligence.