As mentioned in one of the comments to the question, CXO uses the Deep Space Network for communication.
This appears to be reliable resource for the CXO.
According to this and this
|Two low-gain, conical log sprial antennas provide spherical coverage
|Transmit 2250 megahertz (MHz)
|Receive 2071.8 MHz
|2 kilobits persecond (kbps)
|Solid-state recorder; 1.8 gigabits (16.8 hours) of recording capacity
|Selectable rates from 32 to 1024 kbps Downlink data includes pre-recorded engineering and science instrument data interleaved with real-time data
|Data downloaded to Earth typically every 8 hours
According to this
Commands for executing the observing plan are sent from the OCC to one of the three stations in Spain, Australia and California that make up NASA's Deep Space Network, for relay to the orbiting spacecraft.
After carrying out the planned observations, the Chandra spacecraft transmits scientific data and monitoring information to the OCC, via the Deep Space Network, approximately every eight hours.
The communications, control, and data management system is the nerve center of the Observatory. It keeps track of the position of the spacecraft in its orbit, monitors the spacecraft sensors, receives and processes commands from the ground for the operation of the Observatory, and stores and processes the data from the instrument so that it can be transmitted to the ground.
Chandra has two low gain antennae, either one of which may be used for two-way communications with Chandra's Operations Control Center (OCC). All ground commands to and from Chandra along with telemetry data — sent through a set of three NASA ground stations constituting its Deep Space Network — are routed through one of these antennae, typically about once every eight hours.