This paper considers AI-service placement over geographically distributed RAN sites equipped with GPU resources partitioned into fixed, isolated multi-instance GPU (MIG) profiles. We propose C$^2$AIR, a chance-constrained optimization model that maximizes expected AI requests served while protecting uncertain RAN workloads and enforcing probabilistic capacity reliability requirements for admitted AI services. C$^2$AIR allows a service to run at multiple sites and accounts for discrete profile, memory, and GPU-slice constraints. We evaluate C$^2$AIR on a four-site deployment calibrated from NVIDIA Aerial RAN capacity figures and MLPerf Inference results, and on seven larger scenarios with up to 15 sites and 40 AI services, computing every violation and overload probability exactly from the demand distributions. C$^2$AIR keeps the RAN violation probability within its target at every hour of the day, whereas reserving for the mean RAN demand violates it in 24\% to 47\% of the intervals. The reliability condition prevents placing AI models that would be overloaded in 85\% of the intervals at an event hour, and multi-site replication serves 2.7 times more AI requests than single-site deployment. The evaluation also shows that coarse MIG instances and a heavy demand tail can make strict RAN protection expensive.

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