Time is one mechanism through which Indigenous-modern dichotomies are created and maintained and an enduring trope of difference in the settler-colonial imaginary. This article explores the strange temporality of indigeneity within 'progressive' discourses in Australia. Taking Johannes Fabian's concept of 'allochronism' as a point of departure, and drawing on ethnography of non-Indigenous people working in Indigenous health in the Northern Territory, I show how there is a kind of cultural Lamarckianism in operation. 'Western' individuals are seen to inherit the cumulative cultural knowledge, acquired over centuries, of germ theory and responsible alcohol consumption. By contrast, Indigenous people are seen to struggle with banking and infectious diseases because they have not had sufficient time to develop the appropriate cultural knowledge. Through the anthropomorphising of culture and the culturalisation of individuals, the Indigenous person/culture becomes the 40,000-year history of human occupation of the continent. I point to the limits of this settler-colonial imaginary and potential alternatives.