This paper finds that a 1 percent reduction in the cost of exporting or the cost of international transport is associated with an export diversification gain of 0.3 percent or 0.4 percent respectively. Lower domestic market entry costs can also promote diversification, but the elasticity is weaker (-0.1). To obtain these results, the authors construct new measures of export diversification for 118 developing countries using highly detailed 8-digit mirror data from the European Union. The analysis also incorporates new export cost data from the World Bank's Doing Business database, covering document preparation, inland transport, administrative fees, and port/customs charges. Findings are highly robust, including to the use of geography and colonial history as instruments for trade and entry costs. Both the signs and relative magnitudes of these effects are consistent with predictions from a heterogeneous firms model of trade with asymmetric costs.