Kevitz made his international debut at Bradley Beach 1929, with 4/9 for 8th place; world champion Alexander Alekhine won.
[8] In the 16th Marshall Chess Club Championship 1932, Kevitz scored 9/13 for 2nd place, behind Reuben Fine.
[10] In the United States Chess Championship, New York 1936, Kevitz scored 7.5/15 for 8th place, as Samuel Reshevsky won.
In the team match, USA vs USSR at Moscow 1946, Kevitz made the best American result with 1.5/2 against Igor Bondarevsky.
[2] In the Manhattan Chess Club Championship, 1955–56, Kevitz scored 8.5/15 for 6-7th place, and defeated his student, Arthur Bisguier, a future Grandmaster, who was then U.S.
[11] On the first official United States Chess Federation rating list, July 31, 1950, Kevitz ranked third at 2610, behind only Reuben Fine and Samuel Reshevsky.
[12][13] In his later years, Kevitz was active in correspondence chess, often playing under the pseudonym 'Palmer Phar' (he worked at Palmer Pharmacy).