Does an Intervenor get own Peremptory Challenges?

Does an Intervenor have a right to make peremptory challenges in jury selection?

It will depend on whether the court finds the interest of the intervenor is aligned with that of one of the original parties. See:

Anno. 32 A.L.R.3rd 747: No. of challenges allowable in civil cases where more than 2 parties are involved. Citing OK cases: M&D Motor Freight Lines v. Kelley, 1948 OK 128, 202 P.2d 215; Albina Engine & Machine Works, Inc. v. Abel, 305 F.2d 77 (10th Cir. 1962). Where interests of multiple parties identical, only one challenge allowed. Thompson v. Presbyterian Hosp. Inc., 1982 OK 87, 652 P.2d 260, 266-8: Error to grant multiple challenges absent showing of actual, as opposed to potential conflict among defendants.