This paper describes an integrated assessment model with an unknown temperature threshold where severe and irreversible climate impacts, called a tipping point, occurs. The possibility of tipping leads to the following linked outcomes: a prolonged period of peak temperature; a rebound in emissions prior to and during peak temperature; and a fall in the optimal carbon tax as a ratio of output prior to and during peak temperature. Although tipping can occur in any period where temperature rises to a new maximum, the optimal carbon price can be calculated from future temperature outcomes conditional on no tipping. Learning that tipping has not occurred lowers the tax.