Preheat oven to broil. Halve peppers and remove stem and seeds, then place cut-side down on a foil-lined baking sheet. Broil until skin is blistered and blackened.
Meanwhile, melt butter in a saucepan over medium-low heat. Add the onions and cook, stirring occasionally, until caramelized. This will take 20-30 minutes.
When the peppers are done, remove them from the oven and place in a ziplock bag or a bowl with cover. Let the peppers cool until they are cool enough to handle, then peel off the skins and discard. If you have roasted the peppers long enough, the skin should peel easily. If it doesn't come off, don't worry, just proceed.
Chop the peppers coarsely, and when the onions are nicely browned, add the peppers to the saucepan and mix well. Remove pan from heat. Add the cheeses and stir to melt. (You can return the pan to the heat if the cheese isn't melting, but you don't want it soupy.) Once the cheese is melted, season to taste.
Spoon into a serving dish, scatter the chives on top, and serve warm with thick tortilla chips, crostini, or pita chips. This is equally delicious at room temperature or even cold - just note that when cold, you'll need a knife to spread.