Stud service Portland?

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Good bio-security practices would render such a situation poor practice. What you *can* do, though, quite easily is to obtain fertile hatching eggs. The key part of either option would be that your hen would need to be broody (meaning her hormones would be telling her that she wants to set and hatch a clutch of eggs). Some hens seem to be perpetually broody and others go their entire lives without ever having a broody cycle. What breed is your bird? I ask as some breeds are more prone to broodiness than others.
IF your bird goes broody that is when you would need to get the eggs to put under her for hatching.......that can be done by purchasing fertile eggs from a breeder, many hatcheries, individuals in your community who have a flock that does have roosters, etc.
One thing to consider, though, is that there is always a 50/50 chance that the chicks hatched will be male - you say you don't want to have a rooster, so what would you do with male chicks?
Motherhood is not really something chickens aspire to - even when a hen does go broody and hatch chicks she mothers them for a time (some as short as a few weeks, others for a few months) and then those chicks are nothing more to her than just another flock-mate.