Yes. they hunt monkeys and also lower primates like galagos and bushbabies. These lower primates are little but they are not monkeys. They do live in trees. They often hide inside tree holes, and chimps have learned to use sticks to stab and kill them for food. In fact, chimps got the AIDS virus by hunting monkeys that were infected. The chimps suffered a population crash, and only those who had immunity against the AIDS virus survived. Subsequently, we humans hunted chimps for food, and we too got the same virus. Luckily for us, we have made tremendous progress since the 1980s on fighting viral infections and we found out how it is transmitted and so how to avoid being infected, so we are not likely to suffer a similar population crash, even if millions did contract the virus and a large number have died.
BTW, lower primates, including lemurs, are not just small. They have wet noses, like those found in cats, dogs, cows, sheep and most other land mammals, and a narrow crease between the nose and the mouth, known as the philtrum. The philtrum keeps the nose pad wet by transporting water from the mouth to the nose. A wet nose allows mammals to smell better by trapping odor particles in the air. Lower primates also have limited color vision and most are nocturnal. Monkeys, apes and humans are higher primates, with excellent color vision, and a dry nose pad, so that they rely more on the sense of sight than the sense of smell. Looking at the nose therefore allows you to tell whether a small primate is a higher or lower primate.