Slice the cucumber into paper thin rounds on a mandoline and lay the slices flat between two pieces of paper towel. Let the cucumbers drain on the towels for 5-10 minutes so that all of their excess moisture has been absorbed into the towel.
Spread each slice of bread with a thick layer of vegan cream cheese then use a round 2-inch diameter cookie cutter to cut 2 circles out of each piece of bread. Set aside.
Working with one bread round at a time: take 2 cucumber rounds and use kitchen shears to slice one of the rounded edges off to create a straight edge. Lay the slices on the bread round so that the straight edge is almost in the center of the canapé . Repeat this process with the remaining bread rounds.
Sprinkle the canapés with freshly cracked pepper on the sides with the cream cheese exposed then lay a chive directly down the enter of the canapé, clipping any overhang off with kitchen shears. Repeat the process with the remaining canapés.
Notes
If you are not on a vegan diet you can use regular cream cheese or even flavored cream cheese if you would like.