In terms of the theory of identity defined as selfhood or as sameness expounded in ”Oneself as Another” (1992) by Paul Ricoeur (1913-2005), I would like to discuss the problem of identity in St. John de Crèvecoeur's (1735-1813) Letters from an American Farmer (1782). In the fiction, the narrator, the Farmer James who has immigrated into America from France, seems to have determined his identity, but actually, his identity remains in question. His indeterminacy of identity entails a series of questions: How does an European become an American after his immigration? What has he lost or gained in America? Whether or not has he really realized his American dream? Has he encountered any dilemma while determining his identity? How does he compromise the culture of the Old World with that of the New World? Applying Ricoeur's theory of identity to Crèvecoeur's Letters from an American Farmer, I will argue that identity shifts between selfhood and sameness on account of the change of time and space.