According to Training Center XML - Wikipedia it's a particular flavor of xml, and according to that article it's similar to the gpx flavor of xml that Garmin gps units spit out. I'm pretty sure ArcGIS can read a gpx file, so you may want to find a gpx file and compare it to your tcx file and then see if there is a conversion routine available to do so. See this too: TCX Converter - The multiconverter tool
edited to add: GPX to Features tool : GPX To Features—Help | ArcGIS Desktop
Here is what your tcx file looks like in xml notepad:
That should just about do it....