It depends on the region. There are two main variations.
- The "normal"* pronunciation would be like in 'gerne' (or like you would pronounce the 'ck' in the English word 'lick').
- However, in some regions it's pronounced soft like the 'ch' in 'dich'.
*normal, because it follows the default, distinct pronunciation for 'g', whereas (2) makes the 'g' sound like a 'ch', i.e., would mean this is an exception.
From the link guidot points out in his answer, I'd assume the 'officially' (Duden) correct way would be (1) as well, but the rule can also be interpreted in favour of (2).
From the Duden page that guidot linked (http://www.duden.de/sprachwissen/sprachratgeber/zweifelsfaelle-bei-der-aussprache):
"Dasselbe gilt auch für die Buchstabenfolge -ig: Auch hier wird das auslautende -g standardsprachlich nicht wie ein k [k] gesprochen, sondern wie der Reibelaut in dem Wort „ich". Das gilt für Wörter wie König, Honig, eilig, sperrig und viele andere Adjektive auf -ig. Sobald aber durch Deklination weitere Buchstaben hinzutreten, wird das g wieder wie g gesprochen: die Könige, eilige Nachrichten, in einer sperrigen Kiste. Folgt der Endung -ig die Ableitungssilbe -lich (königlich), so wird das g wie ein k [k] gesprochen."
Basically the official rule says: a) In cases of '-ig' at the end of word (like in "heilig") the 'g' is pronounced like a 'ch'. b) If additional letters are added by declination after the 'ig', like in "Könige", the 'g' is spoken like any other 'g', i.e. a little softer than a 'k'. c) If, however, the 'ig' is followed by a 'lich', like in "königlich" the 'g' is pronounced strong like a 'k'.
So in the case of "Heiligtum" I think b) should apply, whereas I ignore that the rule says "if by declination additional letters follow the 'ig'", so one might argue that b) shouldn't apply to "Heiligtum" as the 'tum' part is a suffix not a declination. One might then either argue that the rule does not apply at all, which would mean the normal 'g' pronunciation applies as well. Or one could argue that a) applies to 'Heilig' and its spoken the same if it occurs in a compound word/form.
All in all, I'd say there is about an equally good case to use both, in some region you might get some strange looks with either version. And as the discussions here show, common usage as well as official rule interpretation are debatable even amongst native speakers.
When singing, I'd say, use whichever version of the two that goes better to your melody ;)