As noted above, drain the maraschino cherries, reserving the juice (!), finely mince the cherries, and then pat/squeeze VERY dry. Set aside.
In a large mixing bowl, beat the butter, oil, and sugars until combined.
Beat in eggs, vanilla extract, and cherry extract.
In a large bowl, whisk together flour, baking soda, and cream of tartar.
Add flour mixture to the butter mixture in 2 or 3 additions, beating until just combined after each addition. Do not overmix or dough will be tough.
Beat in cherries until just distributed. Again, do not overmix.
Using a spatula, fold in chocolate chips.
Line baking sheets with parchment paper or silicone baking mats.
Drop dough by teaspoonfuls onto baking sheets.
Bake at 375 for 8-11 minutes, or until edges and bottoms are lightly browned.
Remove to wire racks to cool.