No, the Chronicle is owned by Hearst Communications. Neither firm’s Wikipedia mentions Ron Conway.
San Francisco Chronicle - Wikipedia
The San Francisco Chronicle is a newspaper serving primarily the San Francisco Bay Area of the U.S. state of…
Hearst Communications - Wikipedia
Hearst owns a wide variety of newspapers, magazines, television channels, and television stations, including the San…
Edit: the parent comment previously alleged that Ron Conway owned the Chronicle. Its author removed this claim without mentioning so.