Hi Brian,
Assuming you already have ProPhoto RGB in your system profiles folder, the simplest way of setting up an output recipe in Capture One 8 to do what you want is to go to the Output tab, click on the three dots to the right of the Process Recipes header, then select Add Recipe -> New Recipe (you can also duplicate an existing working recipe and edit that instead, if that would be easier).
The new recipe will initially appear as Untitled Recipe and highlighted in yellow. Left-click once on the recipe name and change it to something useful.
In the second, Process Recipe, subsection, click on the up/down arrows to the right of the ICC Profile dialog box in the Basic tab and select ProPhoto RGB from the list that opens up - it appears near the bottom of the RGB profiles subsection, so you may need to scroll down to find it. Set the other parameters for file format, bit depth etc. as necessary, make sure the selection box to the left of the new recipe is ticked, and you're done.
If you can't locate ProPhoto RGB in the drop-down list of ICC Profiles, there is a remote possibility that it may not be on your system (or not in the system profiles folder) and you might need to install it first.
Hope that does the trick.
Malcolm