Not by a long shot.
A quick perusal of the list maintained by the Minnesota Legislative Reference Library shows that particular 'stained glass ceiling' was broken decades ago, by Sister Michele McGurran. Sister McGurran served two terms as chaplain to the Minnesota Senate, from 1981-1984.
Her initial appointment predated the promulgation of the current Code of Canon Law, which reserves the title of 'chaplain', and consequently appointments to such positions, to priests or bishops. Although this remains a sore point with many lay 'chaplains' working in hospitals and prisons and the like, in those cases there is some logic to it- the sick, dying, and imprisoned need access to the sacraments, and only one capable of the 'full care of souls' can fulfill that requirement. The position of Senate chaplain does not carry the same sacramental responsibilities.
Sister McGurran is, I believe, an OSB (Benedictine) attached to Mount Saint Benedict in Crookston. The Mount used to maintain a house on Summit Avenue where sisters were sent for formation and continuing education.
Sister McGurran was eventually replaced by a Lutheran pastor (the chaplaincy shifts between denominations) and since that time only priests have been appointed, including Father Kevin McDonough (2007-2010) who served during a key point in the Archdiocese of Saint Paul and Minneapolis's efforts to prevent the opening of a civil window for the filing of lawsuits related to clergy sexual abuse. The Minnesota House of Representatives has been even less fortunate in its appointments. 'Charter' priest Reverend Clarence Vavra served as chaplain to that body for a brief period in the 1960s.
If you are looking for a more deserving Catholic institution to donate to this Christmas season, or a way to honor Sister McGurran's ground breaking ministry, I strongly urge you to consider donating to Mount Saint Benedict Monastery.
Read more here: http://www.sacbee.com/news/politics-government/capitol-alert/article4813806.html#storylink=cpy