In many climate model simulations using realistic, time-varying climate change forcing agents for the 20th and 21st centuries, the North Atlantic thermohaline circulation (THC) weakens in the 21st century, with little change in the 20th century. Here we use a comprehensive climate model to explore the impact of various climate change forcing agents on the THC. We conduct ensembles of integrations with subsets of climate change forcing agents. Increasing greenhouse gases -- in isolation -- produce a significant THC weakening in the late 20th century, but this change is partially offset by increasing anthropogenic aerosols, which tend to strengthen the THC. The competition between increasing greenhouse gases and anthropogenic aerosols thus produces no significant THC change in our 20th century simulations when all climate forcings are included. The THC weakening becomes significant several decades into the 21st century, when the effects of increasing greenhouse gases overwhelm the aerosol effects.