From Longman Dictionary of Contemporary Englishon the off chanceon the off chanceHOPEif you do something on the off chance, you do it hoping for a particular result, although you know it is not likely I didn’t really expect her to be at home. I just called on the off chance. → off-chance → chance
Examples from the Corpus
on the off chance• Much effort went into tracing remote family connections abroad on the off chance of identifying a benefactor.• I keep all of my old clothes on the off chance that they might come back into fashion.• I asked him on the off chance.• She thought of ringing him on the off chance of catching him at the flat, but shelved the possibility as unlikely.on the off-chanceon the off-chanceCHANCE/BY CHANCEif you do something on the off-chance that something will happen, you do it hoping that it will happen although it is unlikely I just came to see you on the off-chance that Pippa might be here. → off-chanceExamples from the Corpus
on the off-chance• I called on the off-chance that Patty might be home.• There was no time to contact him, so I came on the off-chance.• I just came on the off-chance.• It was a long way to drive on the off-chance that something would come of it.• The card is too expensive on the off-chance I could get in an away game during the season.• I walked over to the wardrobe and opened the door just on the off-chance.• I rang Otto on the off-chance. 