I use walnut oil. It polymerizes on the
wood and also does not go rancid. It is really the best of the healthy oils to use on wood (unless you are allergic to walnuts). It also has a pleasant smell. Coconut oil is my second pick. It can eventually go rancid but if you use your cutting board regularly you'll need to oil it again before the coconut goes rancid.
You can make a really nice treatment for your board by mixing the oil with melted beeswax (like you are making a comfrey salve or lip balm). The beeswax helps to give a better oiling to the wood.
I definitely use walnut or coconut over linseed.