There is at least one citation reporting death in PubMed.1 I was not able to load the article, but having gone trough related literature on tarantula bites, it seems that a bite often causes localized necrotic ulcers,2 which, although not usually lethal, could lead to infection, gangrene, and death if left untreated.
Some quick digging through newspaper archives reveals more anecdotal references. The Arizona Daily Citizen September 14, 1901 reports:
The bite of a small tarantula cased the death of Gottlieb Hassler, a pioneer of this valley, at this home in Evergreen yesterday afternoon. Last Wednesday Haler went to the barn on his ranch to feed his horses. While getting some hay a tarantula the size of a pigeon's egg and covered with black hair fell on his arm and bit him. Although not especially painful the bite was soon followed by a swelling of the arm to twice its normal size.
A physician was summoned and the wound cauterized, but the action was too late to prevent blood-poisoning. Hasler grew worse rapidly and died yesterday afternoon in terrible agony.
I should note that in this context it is likely that the newspapers are using the word tarantula to refer to a wide range of spiders. The death reports are common enough in the early literature, however. In the words of a headline from The Philadelphia Inquirer on July 17, 1899: "Bitten by a Tarantula, Death Probably Lurked in a Bunch of Bananas."
- Banerjee, K, R Banerjee, A K Mukherjee, and D Ghosh. “Tarantula Bite Leads to Death and Gangrene.” Indian Journal of Dermatology, Venereology and Leprology 63, no. 2 (April 1997): 125–126.
- See for example Isbister, Geoffrey K, and Hui Wen Fan. “Spider Bite.” Lancet 378, no. 9808 (December 10, 2011): 2039–2047. doi:10.1016/S0140-6736(10)62230-1.