Betting the chalk just means playing the favorite, but in my experience its usually only used re taking a heavy favorite on the moneyline. So a chalk parlay is when you string together a bunch of those. For example today i have a parlay of BC, UCF, washington, FSU, okie st and michigan. I took them all on the moneyline rather than the spread so they just need to all win. And they (with the exception of fsu) are all massive favorites at like -500+. Id never risk, say, $500 to win a $100 by betting on one of them on the moneyline, but by stringing a bunch together in a parlay like that you can get a decent payout (the one i have pays 2x) while only losing if there is a big upset.
I do a lot of parlays like that on the heavy chalk in both football and soccer and have a lot of success with them. Of course, big upsets do happen (Vikings last weekend, ODU over VT, Memphis last night) and since it only takes one upset to kill your bet, they are not the absolute lock they often feel like they are when you place them.