Wow! My BIG Bad! Thanks, alexoiu. I read "h170 mb" and found the wrong one without reading all the first post. Revised post follows.
There's an easy solution for you, but the manual info is tricky to decipher. Your mobo is the Gigabyte GA-H170M-DS3H; its manual can be downloaded here:
http://www.gigabyte.com/products/product-page.aspx?pid=5585#manual
See p. 13, Item3/4 for pinout diagrams of the mobo fan headers. It has only one SYS_FAN header, and it shows that its Pin #4 is "VCC", whereas that pin on the CPU_FAN header is "Speed Control". What those mean is that the CPU_FAN header uses PWM Mode to control fans, and that can ONLY control 4-pin fans. However, the SYS_FAN header does NOT put out a PWM signal on Pin #4. In fact, it acts only as a 3-pin fan header using Voltage Control Mode, even though it has 4 pins. Why? To make it easy for people like you who are supplied with 3-pin fans in their cases. This header CAN power AND control both 3-pin and 4-pin fans. So, just plug your three case fans into this SYS_FAN header.
However, to do that you will need a SPLITTER, but NOT the one linked by James Mason above. That device is a HUB, and it only works for 4-pin fan systems and MUST have a PWM signal from the mobo header to work. Here are examples of SPLITTERS with 3 outputs.
http://www.newegg.com/Product/Product.aspx?Item=N82E16812423163&cm_re=coboc_fan_splitter-_-12-423-163-_-Product
http://www.newegg.com/Product/Product.aspx?Item=N82E16812423162&cm_re=coboc_fan_splitter-_-12-423-162-_-Product
(But that first one is currently out of stock at that supplier.)
Anyway, a SPLTTER has only one arm with a female connector to plug into your mobo SYS_FAN header, and two or three output arms each with male (with pins) connectors to plug you fans into. It does NOT have an extra arm with a connector to plug into a PSU power output. A Splitter can only distribute the power from the mobo header to all its fans. So you are limited to using no more fans that the mobo header can supply. Now, a mobo header typically can supply up to 1.0 amps current it total, and most common case fans today draw from 0.1 to 0.25 amps. So, three common fans on one mobo header is quite acceptable, and that meets your needs.
Why a Splitter and not a Hub? A Hub can only work with 4-pin fans and a 4-pin header that is using PWM Mode for control. You have 3-pin fans in your case that can only be controlled by a header using Voltage Control Mode, and that is what your mobo SYS_FAN header does. So the Splitter is the right way to connect your 3 fans to one SYS_FAN header.
The splitter examples I put above are 4-pin units, but that does not matter They will fit with 3-pin fans and do the job properly. Note that, of the three output arms, only one has all its pins; the other two are missing Pin #3. That is proper. The mobo header can only deal with one fan's speed signal coming back from the fan on Pin #3, so the splitter only allows ONE of its fans to send its signal back.
Connecting your three case fans as supplied to your mobo's SYS_FAN header using a Splitter will put them all under automatic control by the mobo.