A nonwoven composite that exhibits latent elastic properties is provided. The composite is formed from an elastic film laminated to a nonwoven web facing. Latent elasticity may be imparted to the elastic film through the combination of a thermoplastic elastomer and a polyolefin capable of forming semi-crystalline domains among the amorphous elastomeric chains. More specifically, the elastic film may be stretched in one or more directions to orient the elastomer chains. Without intending to be limited by theory, the present inventors believe that the oriented state of the chains may be held in place by the relatively stiff semi-crystalline domains of the polyolefin. The stretched elastic film may subsequently be relaxed and bonded to a nonwoven web facing to form the composite. The composite may be later activated (e.g., heated) to shrink the elastic film and provide it with “latent” stretchability. For instance, the composite may be heated at or above the softening temperature of the polyolefin to soften the crystalline domains and allow the chains to return to their unoriented state. As a result of the present invention, the elastic film may be extended and recover from its unoriented state.