Peel and chop the melons into large chunks. To do this, cut off the ends of the melon. Take a paring knife and peel the melon skin starting from the top of the melon and peel to the bottom of the melon. Cut the melon in half across its equator, between the stem and base. When halved, gently scoop the seeds out of each half. Do not scoop too much of the meat from the melon. Discard the seeds and cut the melon into pieces. Place the melon pieces in the blender.
Wash the cucumber and cut the ends off the cucumber. Cut the cucumber into pieces and place it in the blender. No need to peel the cucumber.
Carefully cut the jalapeno in half and remove the seeds and the ribs. Place the jalapeno in the blender.
Add the olive oil, honey, and juice of one lime to the blender.
Blend on high for 2 minutes or until the desired consistency is reached. The consistency should be pourable and smooth.
Refrigerate the gazpacho for a minimum of 4 hours and then serve.