To prepare the grapefruit, use a paring knife to cut about ½ inch off the top and bottom of the citrus. Then remove the skin from the fruit by setting it down on one of the flat surfaces and using the knife, moving downwards into the fruit and cutting only slightly into the flesh.
Once you've removed all of the skin, use the knife to slice each side of each grapefruit segment and gently pop it out. (It's a good idea to do this part over a bowl to save any juice that falls.)
Place the fruit into a small to medium-sized pot as you go. Save the remaining parts of each grapefruit and use your hands to squeeze any juice into the pot. Also, add the juice you saved in the bowl when you cut the fruit. (There should be a lot of excess juice!)
Add the jalapeño, sugar and water to the pot and bring to a boil. Then reduce the heat to a simmer and cook until the mixture becomes thick, about 30 minutes.