Is It possible to patch a crack in a marble threshold?

Epoxy...

This works on granite should work on marble.

You will need nail polish remover to clean the granite surface, straight razor blades, thick super glue (gel), and if you have a darker Granite Countertop you might want to have dark Sharpie marker. Start cleaning your chipped area with nail polish remover. Let the Granite air dry. Tape off the area surrounding the chip and apply just enough glue to fill the chip and rise just slightly above the surface of the stone. Filling the glue up to within flush of the surface of the tape should be sufficient. Once the super glue has completely dried and the tape removed, use a straight razor blade to remove the excess Super glue by “fanning” the excess material away. Wait and allow the glue to cure before cutting with the razor. The time it takes for the glue to cure depends on how deep the chip was, the humidity in the home, etc.(This next step only applies if you have darker Granite) Once desired results are achieved, you may wish to use a colored permanent marker such as a black Sharpie to color the super glue. A Sharpie is permanent and dries quickly. For lighter colored stones, this may not be necessary.

OR you can try this. Works on ceramic may also work on marble.

How to Repair Holes or Cracks in Ceramic Tile

Patching unwanted holes in glazed tile like this can be a tricky proposition. Here's a solution that may not always be perfect, but will make a big improvement. Polyester resin or auto body filler, often used to repair car bodies. Mix up a small batch by adding some hardener and stirring it thoroughly. Using a putty knife, press the resin into the hole slightly overfilling it. Then just as the material begins to harden while it's somewhat rubbery, trim off the excess with a razor blade.

Next use 600 grit sandpaper to sand the filler smooth. Wetting the paper with water makes it work best. Now it's time to try and match the color of the tile. A porcelain touch up kit which is available at most home improvement centers comes with several different colors of paint. You can also use artists acrylic paints available from Michaels, Hobby Lobby, art supply stores, and online.

The trick here is to mix these different colors together until we come up with one that matches the tile. Apply the paint with a small brush. You can test it on a nearby tile. When you get it the way you want it, then just paint over the patch and let that dry. Give it one final sanding with that very fine sandpaper and you'll have, well, maybe not a perfect match, but something that's a heck of a lot better than what you started with.

Best of luck! Keep us posted :)