I say "I own a company", exactly because "I have an internet startup" seems like an eye-roller. I agree with the previous comment: the fact that we're out-of-the-ordinary in Chicago is one of the things I like best about Chicago.

It's basic salesmanship. Phrase things in the way that sounds best (within the bounds of honesty of course). "I have an internet startup" sounds a lot like "I fell for a get rich quick scheme. Would you like to buy some vitamins?"