Pat chicken breasts dry and place in a large resealable plastic bag. Press excess air out of the bag and seal the bag tight. Pound the chicken gently, but firmly, with the smooth side of a kitchen mallet, until individual pieces of chicken are at an even thickness. About 1/2" thick is perfect. Set bag of chicken aside.

In a small bowl, whisk together oil, honey, mustard, and curry powder. Open up bag of pounded chicken breasts and pour honey mustard mixture over chicken. Again, press out the air in the bag and seal it tightly. Turn the bag several times to get the honey mustard mixture all over the chicken breasts. Place bag of chicken in the refrigerator to marinate for 2 to 4 hours.

Remove chicken from refrigerator. Heat grill to medium-high heat, about 385° to 400° F. Make sure grill grates are scrubbed clean and then oiled. (To oil the grates, add some canola oil or olive oil to a small bowl. Then fold a heavy paper towel a few times to make a smaller square. With a tongs, grasp the folded paper towel and dip it into the oil until the paper towel is drenched. Then run the paper towel over the grates, repeating until all grill grates are thoroughly oiled.) 

Place marinated chicken breasts on the pre-heated and oiled grates. Grill for about 3 to 4 minutes on the first side, or until nicely charred. Flip chicken and grill for another 3 to 4 minutes on the second side, until nicely charred and an instant read thermometer reaches 160°F. Then pull the chicken off the grill, to a platter to rest for a few minutes and continue to cook to 165°F. This will help to ensure that your chicken doesn't dry out from over cooking it. Serve while still warm.