My veneer just popped out while eating. It's one piece. Could it be reattached? (Photo)

good news is that , its in one piece. but show it to yr dentist to check any kind of crack or damage. visit dentist as soon as possible , else micro movement will also create issue with recementation. 

Please head to a dentist ASAP and make sure the inside of the veneer is thoroughly cleaned.  If there is any residue, it may not bond well to the tooth.  Here are the suggestions for the best possible adhesion:  the dentist should gently clean any residual cement and debris inside the veneer.  This can be done with a hand instrument and very light air abrasion.  I would then suggest scrubbing the inside of the veneer with a product called Ivoclean, rinse and dry, followed by applying a porcelain silanating agent or primer.  The tooth should be cleaned and "pumiced", followed by direct air abrasion, phosphoric acid etch, GLUMA, a universal bonding agent which is thin ("low film thickness"), and finally a good light cure cement with a solid curing light which will polymerize the cement.  I will stress that all of this should be done with that tooth isolated from the rest of the mouth, and without the presence of saliva.  Otherwise it will hinder the chemistry of the cement.  After the veneer is permanently seated, make sure the dentist checks your bite and to eliminate any interferences so that it does not come out again.  Hope this helps, good luck!