The time at which climate change signal can be clearly distinguished from noise is known as time of emergence (ToE) and is typically detected by a general circulation model (GCM) signal-to-noise ratio exceeding a certain threshold. ToE is commonly estimated at large scales from GCMs, although management decisions and adaptation strategies are implemented locally. This paper proposes a methodology to estimate ToE for both precipitation and temperature at local scales (i.e., river basin). The methodology considers local climatic conditions and unbiased GCM projections to estimate ToE by using the statistical power to find when the climate significantly differs from the historical one. The method suggests that ToE for temperature already occurred in three Chilean basins (Limarí, Maipo, and Maule). However, in terms of precipitation, an earlier ToE is clearly identified for the Maule basin, indicating that risk assessment and adaptation measures should be implemented first in this basin.