Mice are not humans, but I thought the following was interesting based on the fact that nuts are certainly paleo and probably one of our oldest foods.
Kath
Suppression of Implanted MDA-MB 231 Human Breast Cancer Growth in Nude Mice by Dietary Walnut.
Hardman WE, Ion G.
Department of Biochemistry and Microbiology, Marshall University School of Medicine, Huntington, West Virginia, USA.

Walnuts contain components that may slow cancer growth including omega 3 fatty acids, phytosterols, polyphenols, carotenoids, and melatonin. A pilot study was performed to determine whether consumption of walnuts could affect growth of MDA-MB 231 human breast cancers implanted into nude mice. Tumor cells were injected into nude mice that were consuming an AIN-76A diet slightly modified to contain 10% corn oil. After the tumors reached 3 to 5 mm diameter, the diet of one group of mice was changed to include ground walnuts, equivalent to 56 g (2 oz) per day in humans. The tumor growth rate from Day 10, when tumor sizes began to diverge, until the end of the study of the group that consumed walnuts (2.9 +/- 1.1 mm(3)/day; mean +/- standard error of the mean) was significantly less (P > 0.05, t-test of the growth rates) than that of the group that did not consume walnuts (14.6 +/- 1.3 mm(3)/day). The eicosapentaenoic and docosahexaenoic acid fractions of the livers of the group that consumed walnuts were significantly higher than that of the group that did not consume walnuts. Tumor cell proliferation was decreased, but apoptosis was not altered due to walnut consumption. Further work is merited to investigate applications to cancer in humans.