Please ignore but adding the response for any one else -
I was able to resolve this problem by changing the syntax and escaping the double quotes -
curl -H "Authorization: Session 1563d923-6487-40f2-9ef3-1ed65479784e_23787713" -X POST https://api2.clarizen.com/V2.0/services/data/query -d '{q:"SELECT
BillingAddress,BusinessAddress,CreatedBy,CreatedOn,Name,ExternalID,
SYSID,EntityType,LastUpdatedBy,LastUpdatedOn,LastUpdatedBySystemOn,InternalId,LastDateContacted FROM Customer WHERE BillingAddress=\"abc\"",
paging: {"hasMore": false,"limit": 100000}}'