Who could be more at home in ''The World of Sholom Aleichem'' than the inimitable Jack Gilford? Nobody, that's who. So it is, as they say, a pleasure and a privilege to welcome back Mr. Gilford as the star of a beguiling entertainment in which he first appeared nearly a generation ago. At the Rialto Theater he heads the casts of the four sketches that Arnold Perl adapted from Aleichem's writings and other Jewish sources. The result is an evening of quiet pleasures and recurring rewards.
An aisle-strolling accordionist establishes the folkish tone of the occasion, sets the audience clapping rhythmically, and warms things up for the genial introduction by Joe Silver as Mendele, the Book Seller. What unfolds thereafter is a series of small tales and tall tales in a wryly humorous, sometimes touching vein.
The highlight of ''A Tale of Chelm'' is Mr. Gilford's comic miming as he struggles with a resistant billy goat in a series of transactions illustrating the monumental stupidity of the Chelmites. When the townspeople ask their rabbi why the sea is so salty, he attributes it to the abundance of herring in the water. In ''The Bandit,'' Mr. Gilford's Aleichem explains the precariousness of the writer's trade to a would-be thief (Mr. Silver).
The histrionic appeal of ''Bontche Schweig,'' by I. L. Peretz, lies in the eloquent quietude with which a dumbstruck Bontche reacts to his first taste of heaven after an earthly life of misery and deprivation. The Gilford delivery of Bontche's single line is a poignant conclusion to the beatific parable.