Chipotle Mexican Grill slipped 5 percent lower after its quarterly earnings report Tuesday, and CNBC "Fast Money" traders stood divided over how to trade the stock.

The chain beat Wall Street's profit estimates but fell short of projections for revenue and comparable sales, a key data point for the industry. For trader Steve Grasso, the stock's past performance shows that fear may be overplayed.

"People have bet against this stock time and time again and they've lost," Grasso said.

Read MoreChipotle disappoints Street on key sales metric

Chipotle dropped to about $655 per share in extended trading Tuesday. The stock may jump 10 percent from there, Grasso noted.

Trader Tim Seymour, though, said he would sell at that level. He called Chipotle's comparable sales—which rose 10 percent in the quarter—"unsustainable."

Trader Guy Adami looked for a different chain to rally off of Chipotle's earnings. If Jack in the Box does not get "whacked" in Wednesday trading, it could rally, he contended.

As Chipotle sagged in post-earnings trading, Yum Brands popped. After same-stores sales dropped in its key China market fell less than expected, Yum's stock climbed 4 percent higher.

Read MoreYum profit beats as China sales fall less than forecast

Seymour contended that Yum will likely hit a floor at $80 per share, about $4 lower than where it traded after-hours Tuesday.

"The risk-reward looks very interesting," he said.

In trading a chicken chain, trader Brian Kelly preferred El Pollo Loco. The stock closed about half a percent lower on Tuesday, below $29 per share.

Disclosures:

Tim Seymour

Tim Seymour is long APC, T, BAC, C, DAL, DIS, XOM, F, GE, GM, GOOGL, INTC, EWZ, SCTY and SUNE. Tim's firm is long BABA, BIDU, TUR, MCD, NKE, NOK, SBUX and YHOO. Today, his firm bought YHOO.

Steve Grasso

Steve Grasso is long AAPL, BAC, BTU, EVGN, MJNA, PFE, T, TWTR and GDX. His firm is long AMZN, ICE, AMZN, MCD, NE, OXY, RIG, VALE, FCX and TSE. His kids own EFG, EFA, EWJ, IJR and SPY.

Brian Kelly

Brian Kelly is long BTC=, CTRL calls, GSG, BBRY, SPY puts and U.S. dollar. He is short 30-year bond futures. He is short Australian dollar. He is short yen. He is short yuan.

Guy Adami

Guy Adami is long CELG, EXAS and INTC. Guy Adami's wife, Linda Snow, works at Merck.