"The 'hot' sensation produced by exposure to pepper is apparently due to two natural carcinogens: capsaicin in chili type peppers and safrole in black/white pepper. There are four cookeries in the United States that are noted for their high pepper content: Mexican-American, Cajun, white Creole, and black Creole. Each is largely confined to a single ethnic-cultural group which is concentrated in some counties. By use of county population and mortality data, significantly higher rates for stomach and liver cancer were found in counties inhabited by these four ethnic-cultural groups than in matched control counties."
Could it be true: chilies are carcinogenic? Might as well go to the source to find out, the country where chilies originated: Mexico. A Mexican study looking at associations between gastric cancers, chili consumption and H pylori infection found no independent association between the chilies and the Hp but a weak association with gastric cancer in heavy chili eaters (OR = 1.71; 95% CI = 0.76-3.88, p=0.026).
However there is mounting evidence that chilies may do more good than harm. Spices in general seem to make good candidates according to this recent review:
"the potential of turmeric (curcumin), red chilli (capsaicin), cloves (eugenol), ginger (zerumbone), fennel (anethole), kokum (gambogic acid), fenugreek (diosgenin), and black cumin (thymoquinone) in cancer prevention has been established."
You don't have to look very hard to find that in fact capsaicin has potential to inhibit the proliferation of cells in endometriosis , inhibit the growth of androgen-independent p53 mutated prostate cells, kill melanoma cells etc... The mechanism seem to included apoptosis, autophagy and ROS generation.
All this to say, you can eat your chilies without worrying too much about cancer, the harm done is mostly temporary and the jury is still out for the longer term...