How does a dance company know when it’s really made the big time? Performing works by great choreographers like Twyla Tharp is grand, but it’s not the big time–no, you’ve got to perform in New York City, the dance capital of the world, get rave reviews, and sell out houses. Not an easy task. But Hubbard Street Dance Chicago–known and respected around the world–finally did just that last fall, filling the Joyce Theater to capacity. Now the company comes home to a four-week season with the Spring Festival of Dance, presenting its well-known repertoire of Tharp classics and a new dance, James Kudelka’s Heroes, that the New York critics loved, as well as standards from Margo Sappington, Daniel Ezralow, and artistic director Lou Conte. One of the most enticing pieces, however, is the company premiere of Kevin O’Day’s Quartet for IV (and Sometimes One, Two or Three), a delicate, soulful piece first performed here last summer by the White Oak Dance Project. All these dances are spread over six different programs, a fact that could complicate a person’s life. Hell, go twice. Opening-night gala Wednesday at 7 (see listing for details); performances continue through May 14. At the Shubert Theatre, 22 W. Monroe; $12-$38. Call 902-1500 for tickets and info, 663-0853 for group sales and multiple-performance discounts.