**Larry Padwa Answers:**

In the complete Hebrew Calendar cycle of 689472 years, the first day of
Chanukah falls on Shabbat 127139 times, which is about 18.4% of the time.

To validate this with smaller numbers, in the past century (1900-1999)
the first day of Chanukah fell on Shabbat 19 times (including today).

Note, however, that the distribution is highly irregular. During the
current century there were two occasions of two consecutive years of the first day of
Chanukah on Shabbat (1904-1905 and 1931-1932), and one occasion where there was an
interval of sixteen consecutive years without the first day of Chanukah on Shabbat
(1936-1951)