Am I going to lose my financed car if I file a chapter 7 bankruptcy?

No, you don’t automatically lose it just because of the bankruptcy.  You can pay for it and keep it, or give it up.  The choice is yours.  

When you file a chapter 7 case, you list your secured debts (like car loans, mortgages, financing/purchase contracts for furniture) in the bankruptcy, and then you state whether you want to surrender or retain the collateral.  If you want to surrender it, then you stop making payments.  Eventually they will repossess your car, and the balance is wiped out by the bk.

If you want to retain it,  you list the loan in the bankruptcy, and then you check a box that states that you want to keep the car and keep making payments on it.  This is called your Statement of Intention.

Normally, when you keep a car loan, you sign a reaffirmation agreement (after you file bankruptcy), which obligates you to the same payments, same interest rate, same balance, same everything.  It is very unusual for a creditor to change any of the terms for you (like lowering the interest rate).  Don’t hold your breath on changing any of the terms.

Don’t just take my word for it.  The Utah Bankruptcy Court has a fairly clear description of reaffirmation agreements here:

Reaffirmation Agreement
A debtor in a bankruptcy case may decide to remain legally obligated to pay a debt that would otherwise be discharged in bankruptcy. This is called reaffirming a debt. Reaffirming a debt is voluntary; debtors are not required to reaffirm any debt.

The reaffirmation of a debt is governed by 11 U.S.C. § 524(c), (d), and (k). A Reaffirmation Agreement is enforceable only if it complies with these Bankruptcy Code provisions. For example, any agreement to reaffirm a dischargeable debt must be entered into before the debtor receives a discharge.

Instructions for filling out a Reaffirmation Agreement form are avaialble here.

Debtors who are NOT represented by an attorney MUST also file a Motion for Approval of Reaffirmation Agreement. Upon receipt of the motion for approval, a hearing will be set and notice of that hearing will be mailed to the debtor and the creditor. The Debtor MUST attend the hearing to have the reaffirmation agreement approved.

And a sample reaffirmation agreement here.

Now of course there are all kinds of potential pitfalls with keeping the car.  You have have too much equity, or too little income, or other loans with the credit union which are cross-collateralized with the car.  But this is a bit more complicated and you’ll need to work it over with your attorney.