We present late-time optical and mid-infrared observations of the Type II supernova 2003gd in the galaxy NGC 628. Mid-infrared excesses consistent with cooling dust in the ejecta are observed 499 to 678 days after outburst and are accompanied by increasing optical extinction and growing asymmetries in the emission-line profiles. Radiative-transfer models show that up to 0.02 solar masses of dust has formed within the ejecta, beginning as early as 250 days after outburst. These observations show that dust formation in supernova ejecta can be efficient and that massive-star supernovae could have been major dust producers throughout the history of the universe.