If the piece isn't too long and you have only note information (no controllers etc) you may just do it manually. Open the event list editor, set it to show only notes, cmd-click every odd note and when you are done change the MIDI channel of the selected notes at once.
Afterwards activate the region and go to the local edit menu:
Edit -> Separate MIDI Events -> By Event Channel
This creates a new track with a new region and distributes your
notes based on their MIDI channel across the two regions:
You may run into a problem if you have other events than notes only. This can make the selection process very tedious if not impossible.
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If you are familiar with the Logic Environment and MIDI routing in Logic, you can do the classic hocketing in the Environment. Connect the output of your instrument channelstrip to a transformer which is set to "Alternate Split". Send the two outputs on different channels to an IAC bus (or something else you may prefer) and record both to a new track and split by event channel as usual.
Due to the simple "Alternating Split" function you cannot tell in advance which region will contain even or odd notes but you will certainly find this out afterwards ;-)
If Logic X tends to go crazy during the recording process (mine does), just disable the playing instrument. The notes come out of the channelstrip anyway.
Attention:
Hocketing in the Environment by "Alternating Split" distributes all events, not just notes. Make sure that you actually process only notes, it may be necessary to block everything else with another transformer in front.
If you need to deal with controllers, pitch bend, aftertouch etc., the whole process gets complicated. Depending on the difficulty you may be able to do it in Logic or would need to use a specialized program. But I think complex hocketing including controller events isn't easy in any program depending on the type and distribution of the events.