Vertical Endeavors, a St. Paul-based chain of rock climbing clubs, is putting the finishing touches on its newest gym near Chicago, with 44,000 square feet of wall space. Local website MySuburbanLife.com has a preview of the new Vertical Endeavors in Glendale Heights. When it opens in August, it will be the nation's biggest rock-climbing facility. It's the second Illinois site for Vertical Endeavors, which also has locations in Minneapolis and Duluth. The chain posted a video of the early stages…