According to the Greek Orthodox Church can one marry a Maronite Catholic? Is a wedding between a Greek Orthodox to a Maronite Rite Catholic permitted and can the ceremony be performed in the Greek Orthodox Church?
According to the Greek Orthodox Church can one marry a Maronite Catholic?

The short answer is yes.


  When getting married in the Greek Orthodox Church, especially interfaith marriages, there are a lot of questions about what may be allowed in the Church, and what may be prohibited. Luckily, as with many practices of the Church, the Church has explicitly stated guidelines for marriage in the Greek Orthodox Church.
  
  These guidelines outline the official position of the Orthodox Church and simply dictate what is allowed and what is not allowed to take place. They concern the basic rules that must be met, acting as the official canons of the Orthodox Church. They represent the fundamental core of the sacrament of marriage where there is little to no room for negotiation or exception.
  
  According to the Greek Orthodox Church, first and foremost, the marriage must be conducted in an Orthodox Church. This unfortunately pretty much rules out the romantic beach weddings in the Caribbean that are all over TV. This is not because the Church does not like the beach; rather since Marriage is one of the seven sacraments, it is seen as a sacred ceremony, one that should be conducted in a sacred space—an Orthodox Church.
  
  This in turn means that an Orthodox priest must celebrate the sacrament with a traditional Orthodox ceremony in an Orthodox Church. The respective Diocese must also grant authorization of the service.
  
  The engaged couple must meet with the parish priest of the church in which they are to be married. The priest must belong to the Greek Orthodox Archdiocese; however marriages that are performed in another Orthodox jurisdiction (Serbian, Russian, Bulgarian etc.) in communion with the Greek Orthodox Church are recognized as valid. Before asking for authorization from the Bishop, it is the priest’s job to verify that several fundamental conditions are either avoided or met adequately. - Getting Married in the Greek Orthodox Church


For the Catholic party, the future spouse must obtain a dispensation from their local ordinary (bishop), in order to make it a valid canonical marriage.


  Can.  1127 §2 If grave difficulties hinder the observance of canonical form, the local ordinary of the Catholic party has the right of dispensing from the form in individual cases, after having consulted the ordinary of the place in which the marriage is celebrated and with some public form of celebration for validity. It is for the conference of bishops to establish norms by which the aforementioned dispensation is to be granted in a uniform manner.
   The Code of canons of Oriental Churches (CCEO) has this to say on Marriage:
  
  Canon 813 Marriage between two baptized persons, one of whom is Catholic and the other of whom is non-Catholic, is prohibited without the prior permission of the competent authority.
  
  Canon 814 For a just reason the local hierarch can grant permission; however he is not to grant it unless the following conditions are fulfilled: the Catholic party declares that he or she is prepared to remove dangers of falling away from the faith and makes a sincere promise to do all in his or her power to have all the offspring baptized and educated in the Catholic Church; the other party is to be informed at an appropriate time of these promises which the Catholic party has to make, so that it is clear that the other party is truly aware of the promise and obligation of the Catholic party; both parties are to be instructed on the essential ends and properties of marriage, which are not to be excluded by either spouse.
  
  Canon 816 Local hierarchs and other pastors of souls are to see to it that the Catholic spouse and the children born of a mixed marriage do not lack spiritual assistance in fulfilling their spiritual obligations, and are to assist the spouses in fostering the unity of conjugal and family life.
  
  Canon 835 Dispensation from the form for the celebration of marriage required by law is reserved to the Apostolic See or the patriarch, who will not grant it except for a most grave reason.