Iivo Nei (born 31 October 1931 in Tartu) is an Estonian chess master.
In 1947, at the beginning of his career, Nei took 3rd in Leningrad (Saint Petersburg) at the sixth USSR juniors championships. The event was won by Viktor Korchnoi. In 1948, he tied for first with Korchnoi in Tallinn (seventh USSR juniors championships). Nei won the Estonian Championship eight times (1951, 1952, 1956, 1960–1962, 1971, and 1974). In 1955, he tied for third through sixth place in Pärnu (Baltic Republics championships). The event was won by Paul Keres. In 1960, he tied for 14–15th at the 27th USSR championships in Leningrad. The event was won by Korchnoi. In 1961, he won in Palanga (Baltic Republics championships). In 1962, he won in Tartu. In 1963, he won at the Baltic championships in Estonia. In 1964, he won in Pärnu (Baltic championships). In 1964, he tied for first with Keres in Beverwijk. In 1965, he took second, behind Vladas Mikėnas, in Palanga (Baltic championships).