Using a mandolin or a sharp knife, slice the sweet potatoes, carrots and zucchini into thin disks, about 1/16th-⅛th inch in thickness.
In a large mixing bowl, whisk together the almond butter and maple syrup. Add the vegetables and toss until evenly coated. Season with the paprika and salt, tossing once more.
Arrange the vegetables on a non-stick baking sheet or baking paper in a single layer. Bake in the oven for 50 minutes - 1 hour, rotating the tray every 8-10 minutes. Flip the chips halfway through. Keep an eye on them, particularly after the 40 minute mark. If any of the chips start to crisp up before the others, remove them from the oven.
When the chips are golden and crispy around the edges, allow them to cool for a minute and serve. Store in an air-tight container for up to a week.