Nulling interferometry, a proposed technique for dimming a star relative to its surroundings by destructively interfering the light collected by two individual telescopes [Bracewell, Nature 274, 780-781 (1978); Shao and Colavita, Ann. Rev. Astron. Astrophys. 30, 457-498 (1992)], has the potential to permit the direct detection of nearby extrasolar planets. However, because of the extremely high degree of symmetry required for useful levels of starlight nulling, the technique remains in its infancy. We present results of laboratory experiments with a rotational shearing interferometer that are aimed at demonstrating the feasibility of deep nulling at the levels needed for direct planet detection. Our first results include the successful nulling of red laser light to a part in 10(5) and the stabilization of the null leakage to a part in 10(4).