By Noel Randewich

SAN FRANCISCO (Reuters) - Shares of Chipotle Mexican Grill <CMG.N> appear expensive as Wall Street awaits fresh data on the burrito chain's struggle to recover from a string of food-borne illness outbreaks.

Sales data for May, which analysts believe the company might release in the next several days, could provide evidence of whether two-for-one deals are successfully luring customers back after Chipotle posted its first-ever loss in the first quarter.

Its same-restaurant sales may have fallen 20 percent year-on-year in May, according to the consensus of analyst estimates tracked by Thomson Reuters. Chipotle does not normally provide mid-quarter updates, but it has done so occasionally in recent months in order to increase transparency around the crisis.

Shares of Chipotle have dropped 40 percent since August after norovirus and E.coli outbreaks at some of its outlets led to a plunge in sales for the company, which markets its burritos and tacos as healthier than rivals' food.

Estimates for Chipotle's earnings per share for this year have fallen much further than its stock price. Wall Street has slashed its average earnings estimate for 2016 to $4.81 per share from over $20 before the food safety crisis, according to Thomson Reuters data.

Chipotle's stock is now trading near 55 times the next 12 months' expected earnings, its priciest multiple since just after the Wall Street favorite listed its stock a decade ago.

But with investors viewing 2016 as a near write-off for Chipotle because of the food contamination crisis, many are focusing on earnings expectations for next year, when profits are seen rebounding to $11.86 per share.

Based on that figure, Chipotle's stock is trading at a less stratospheric PE of 35, suggesting Wall Street is optimistic about the speed of the company's recovery.

"We're debating visibility of the next month, let alone next year," said Cowen and Company analyst Andrew Charles. "But we think they're going to move more toward normalized earnings as time progresses, and time will help heal the wounds."

Still, a federal criminal investigation, a potential rebound in commodity prices and rising minimum wages are major threats to Chipotle's future earnings potential, cautions Maxim analyst Stephen Anderson.

Chipotle's stock has lost 6 percent since its disappointing first-quarter report on April 26. On Thursday it fell 2.52 percent to $418.36.

Only a few restaurants' shares trade at PE multiples greater than Chipotle's. They include Shake Shack <SHAK.N> at 78, Zoe's Kitchen <ZOES.N> at 210 and Noodles & Co <NDLS.O> at 125, according to Thomson Reuters data.

(Reporting by Noel Randewich; Editing by Dan Grebler)