Heat a grill or broiler to high. Slice kernels from 3 ears of corn and add to a large bowl. Grill or broil the remaining 3 ears until lightly charred all over. Let cool enough to handle, then slice kernels off the cob and add to the bowl with the raw corn.
Add the avocados, 1 tablespoon of the olive oil, half the lime juice, and a pinch of salt to a food processor or blender. Puree until completely smooth. Add 2 tablespoons of the avocado puree to the bowl with the corn. Set the remainder aside.
To the bowl with the corn, add the remaining 3 tablespoons olive oil, the remaining lime juice, honey, chipotle chili powder, smoked paprika, and chopped jalapeño.
Season generously with salt and pepper and toss everything to combine.
Stir in the chopped fresh chives.
Spoon the reserved avocado puree into the bottom of a serving bowl and top with the corn salad. Serve immediately.