We present results from an HST/ACS imaging study of the metal-poor blue compact dwarf galaxy SBS 1415+437. It has been argued previously that this is a very young galaxy that started to form stars only less than 100 Myr ago. However, we find that the optical color-magnitude diagram prominently reveals asymptotic giant branch and red giant branch (RGB) stars. The brightness of the RGB tip yields a distance of 13.6 Mpc. The color of the RGB implies that its stars must be older than approximately 1.3 Gyr, with the exact age depending on the assumed metallicity and dust extinction. The number of RGB stars implies that most of the stellar mass resides in this evolved population. In view of these and other HST results for metal-poor galaxies it seems that the local Universe simply may not contain any galaxies that are currently undergoing their first burst of star formation.