The 1–2 September 1859 magnetic storm was the most intense in recorded history on the basis of previously reported ground observations and on newly reduced ground-based magnetic field data. Using empirical results on the interplanetary magnetic field strengths of magnetic clouds versus velocities, we show that the 1 September 1859 Carrington solar flare most likely had an associated intense magnetic cloud ejection which led to a storm on Earth of D_ST ∼ −1760 nT. This is consistent with the Colaba, India local noon magnetic response of ΔH = 1600 ± 10 nT. It is found that both the 1–2 September 1859 solar flare energy and the associated coronal mass ejection speed were extremely high but not unique. Other events with more intense properties have been detected; thus a storm of this or even greater intensity may occur again. Because the data for the high-energy tails of solar flares and magnetic storms are extremely sparse, the tail distributions and therefore the probabilities of occurrence cannot be assigned with any reasonable accuracy. A further complication is a lack of knowledge of the saturation mechanisms of flares and magnetic storms. These topics are discussed in some detail.