In children and adults, naming an item occasionally interferes with later efforts to name other items. Adult speakers meet with cumulative semantic interference, interpreted as the result of incremental learning. Studies to date have not explored whether incremental learning can also account for interference in children. This inquiry explored context effects on picture naming in 3-year-old children, and explored whether children, like adults, display interference that is semantically based and cumulative. Children named pictures from semantically homogeneous and mixed sets. Reply latency, precision, and repetition errors were recorded. The results showed a progressive slowing of replies in the semantically homogeneous condition that was greater than that observed for the mixed condition. There were no significant effects for precision. Repetition errors, although infrequent, patterned similarly to prior reports for adults. The results pointed out that preschool-aged children meet with cumulative semantic interference in naming, and propose that incremental learning may account for interference effects across evolution.