Preston Nelson, Libertarian nominee for U.S. House in the Illinois 8th district, polled 29.1% in a two-way race against a Democrat. See the returns for all the Illinois U.S. House races here.
This is the highest percentage for a candidate for U.S. House in Illinois who was not the nominee of the Democratic or Republican Parties since 1914, when Progressive Party nominee Ira Copley was elected with 40.8% of the vote.
The 8th district is in the Chicago suburbs.
I think the fellow in Arkansas is the highest for US Senator (LP).
What was the highest for US House by an LP candidate ever?
Joel Balam, Kansas district 3, 2012 – 31.55%.
29.1% would be good for 2nd best.