I stumbled upon this article and found it really an eye opener. I used to think that some things in the bible was cultural and was only applicable in the past, therefore not relevant to us now. The chapel veil was one of the things. The reason of wearing the veil is explained through the incarnation of Christ and His real presence in the Blessed Sacrament.
As explained in the article, Saint Paul outlined a deep theological purpose for keeping the custom that transcends all local and cultural reasons. Therefore all Christian women are Scripturally encouraged, by Saint Paul himself, to keep the custom.
But I want you to realize that the head of every man is Christ, and the head of the woman is man, and the head of Christ is God. Every man who prays or prophesies with his head covered dishonors his head. But every woman who prays or prophesies with her head uncovered dishonors her head—it is the same as having her head shaved. - 1 Corinthians 11:3-5
Am still pondering about this new found understanding...