There are a couple of ways to assign a chopped loop to a single patch.  The easy way is to use the unit itself (with version 1.03 and higher only):

1. Sample a loop.
2. From PATCH/SAMPLE mode, hold SHIFT and press pad 4.
3. Cursor right until you see "Chop [ENTER]".  Press ENTER.
4. Select the chop type and press ENTER. The loop will be chopped and applied across the pads within the same patch/part/track.
5. Write the patch/sample.

You can also use the editor to manually assign chopped snippets to a track, but only from the editor, and only on a rhythm set, not a patch:

1. In the MC-808 editor, press the EDIT button for any part assigned a rhythm set.  Select the WG (Wavegroup) submenu.
2. Select the pad you'd like to assign a chopped snippet to in the upper right-hand pull-down menu.
3. Disable all tones except for Tone 1.
4. Manually assign the wavegroup and sample to Tone 1.
5. Write the patch/sample.