For the fondue:
In a bowl toss together cheeses and cornstarch.
Bring beer to a low boil and stir in the cheese mixture by handfuls, stirring constantly, adding more as the previous mixture has melted. Bring mixture to a bare simmer over moderate heat, stirring, and stir in the rum, cumin and chilies. Taste and add more chilies if desired.
Transfer fondue to a fondue pot and set over a low flame.
For 6 servings, you will need about 2 - 3 cups of cubed chicken, 4 - 5 cups of prepared vegetables and one large loaf of bread, cubed.
grilled chicken, cubed
red and green bell peppers, cubed
jicama tossed with lime juice
blanched vegetables such as asparagus or broccoli
One loaf of your favorite, fresh baked bread, cut in chunks or cubes
*available at Hispanic markets and some specialty foods shops