Canon Rosie Harper supports giving terminally ill people the right to end their lives up to six months early.
A bill on the issue is due to be debate in the House of Lords on Friday.
Yesterday a letter, signed by the Archbishop of Canterbury and more than 20 other faith leaders, was published which said approving assisted dying would be a "grave error".
"If enacted, this bill would have a serious detrimental effect on the well-being of individuals and on the nature and shape of our society," it said.
Canon Harper claims the Church hierarchy is out of touch with the opinion amongst congregations.
She told The Telegraph:
"Some of the stuff coming out of the leadership is simply scaremongering."
"They are using very emotive language and it doesn't help us have a calm conversation about assisted dying.
"I was surprised at the tone being taken on this subject. They start the conversation by saying 'we all know Christian believe ...' when that's not at all the case.
"In fact many Christians believe it's the honourable and compassionate way of treating people."
She's the chaplain to the Rt Rev Dr Alan Wilson, the Bishop of Buckingham. He became the first serving bishop to back the bill earlier this week.
He spoke on Premier's News Hour about his decision: "I have come to support assisted dying, not assisted suicide, precisely because I do believe strongly in the sanctity of life.
"Part of honouring this is respecting people's integrity to make decisions about themselves.
"If Britain really does contain 500,000 old people who want out because they're treated so poorly the answer seems to me to improve their lives not degrade their deaths.
"If we got a huge influx of requests under the Falconer rules, we ought to ask ourselves why and what we're going to do about it, not sweep everything under the carpet by preventing them from expressing their reaction to being treated poorly.
"That in itself is only another form of disrespect.
"I think there is a discussion to be had of the sort that is going on right now that I actually think matters and has to be had and religious figures should not think is taboo."
Canon Harper also told the newspaper some of her parishioners support her view: "I thought people would be furious with me for speaking in support of assisted dying, but I've had many people coming up to me to shake my hand and say 'It's what I've always thought'.
"I fear the church leadership will find itself out of step on this issue, just as it did until this week on women bishops." She said.