Antibiotic resistance is a growing impediment to the control of infectious diseases worldwide, tuberculosis (TB) being among them. TB kills two million people each year and foci of multidrug-resistant TB (MDR-TB) have been identified in Eastern Europe, Africa, Asia, and Latin America. A critical question for health policy is whether standardized short-course chemotherapy for TB, based on cheap first-line drugs, can prevent and reverse the spread of drug resistance. Here we use mathematical modeling, in conjunction with treatment results from six countries, to show that best-practice short-course chemotherapy is highly likely to bring strains resistant to either of the two key drugs isoniazid and rifampicin under control and to prevent the emergence of MDR-TB. However, it is not certain to contain MDR-TB once it has emerged, partly because cure rates are too low. We estimate that approximately 70% of prevalent, infectious MDR-TB cases should be detected and treated each year, and at least 80% of these cases should be cured, in order to prevent outbreaks of MDR-TB. Poor control programs should aim to increase case detection and cure rates together for three reasons: (i) these variables act synergistically; (ii) when either is low, the other cannot succeed alone; and (iii) the second-line drugs needed to raise MDR-TB cure rates are few and extremely costly. We discuss the implications of these results for World Health Organization policy on the management of antibiotic resistance.