He played in many Chilean Chess Championships. In 1932, he took 4th place. In 1934, he took 2nd, behind Mariano Castillo. Finally, Letelier was Chilean Champion in 1957, 1959, 1960, 1964, and 1973. He played for Chile in seven Chess Olympiads.
In tournaments, Letelier tied for 11-12th at Mar del Plata 1936. In 1937, he took 2nd, behind Rodrigo Flores, in São Paulo. In 1938, he tied for 12-14th in Montevideo. In 1945, he took 5th in Viña del Mar. In 1945, he tied for 2nd-5th with Carlos Skalicka, Enrique Reinhardt and Moshe Czerniak in Quilmes. In 1946, he tied for 1st with Skalička, followed by Movsas Feigins, Jorge Pelikán, etc., in Buenos Aires. In 1946, he took 3rd, behind Gideon Ståhlberg and Herman Pilnik, in Paraná. In 1946, he took 11th in Mar del Plata. In 1947, he took 2nd, behind Ståhlberg, in Buenos Aires. In 1947, he took 4th in Buenos Aires. In 1948, he tied for 4-5th in Buenos Aires. In 1949, he tied for 6-9th in Mar del Plata. In 1949, he tied for 2nd-3rd, behind Guimard, in Velez Sarsfield. In 1950, he tied for 5-7th in Venice. In 1951, he took 8th in Mar del Plata/Buenos Aires. In 1951/52, he took 3rd in San Rafael. In 1952, he tied for 11-13th in Mar del Plata. In 1953, he tied for 6-7th in Mar del Plata. In 1954, he won, ahead of joint runners-up Ossip Bernstein and Miguel Najdorf, at the Gran Torneio Internacional Unesco in Montevideo. This was Letelier's finest tournament win. Letelier beat both grandmasters in the field, Najdorf and Bernstein! In 1955, he took 12th in Mar del Plata. In 1957, he tied for 7-8th in Rio de Janeiro. In 1958, he tied for 11-12th in Mar del Plata. In 1959, he took 7th in Lima. In 1959, he tied for 9-10th in Santiago. In 1959, he took 5th in Mar del Plata. In 1960, he took 4th in Asunción. In 1960, he tied for 8-10th in São Paulo. In 1960, he took 7th in Mar del Plata. In 1961, he took 6th in Santa Fe. In 1961, he took 6th in Mar del Plata. In 1962, he tied for 15-16th in Mar del Plata. In 1963, he tied for 3rd-5th in Havana. In 1963, he took 13th in Havana. In 1964, he took 17th in Buenos Aires. In 1964, he tied for 17-18th in Havana. In 1964, he took 5th in Jerusalem. In 1965, he took 9th in Santiago. In 1966, he tied for 10-11th in Havana. In 1967, he took 15th in Havana. In 1969, Letelier won the 2nd edition of the annually played international Mar del Plata Open. In 1971, he took 15th in Havana. In 1972, he tied for 6-9th in La Serena. In 1975, he tied for 8-11th in Buenos Aires. Letelier was awarded the International Master title in 1960.
