user35202: I am creating a standalone Arduino using Atmega328P. The circuit is below.

However, I'm seeing 
avrdude: Device signature = 0x000000 error 

whenever I try to burn the Arduino Uno bootloader. I'm assuming that the chip isn't responding to the SPI lines?
I know I'm doing something wrong but I can't see it.
My connections are 
SCLK --> Arduino Pin 13
MISO --> Arduino Pin 12
MOSI --> Arduino Pin 11
Reset --> Arduino Pin 10

VIN --> 5V
GND --> GND

I'm using a true Arduino UNO as the ISP. I've uploaded the ArduinoISP code into it, choose Arduino as ISP as Programmer and Arduino Uno on boards. The programming connections are just wired from Arduino UNO pins to some vias I've purposely added on the layout.
As mentioned in the comments, I'm adding an image of the layout here.  

I've tried this very circuit on an atmega328P soldered in a TQFP adapter and with the other components soldered on the adapter as well (looks like a jungle of wires) and somehow I was able to burn the bootloader. 
Hoping someone can point out what's wrong.

user35097: It seems that you are using a lm317 voltage regulator to power your atmega328p MCU but I think you forgot the part that lm317 needs feedback of 1.25v with voltage divider network to set its variable output voltage in the schematic you have connected adj pin of  lm317 directly to GND.
S0 check your output vtg from your regulator and another issue voltage regulator only works great when difference between regulating voltage is lower then the supply voltage. 

35202: <p>I am creating a standalone Arduino using Atmega328P. The circuit is below.</p>

<p><a href="https://i.stack.imgur.com/2NQPO.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/2NQPO.png" alt="enter image description here"></a></p>

<p>However, I'm seeing </p>

<pre><code>avrdude: Device signature = 0x000000 error 
</code></pre>

<p>whenever I try to burn the Arduino Uno bootloader. I'm assuming that the chip isn't responding to the SPI lines?</p>

<p>I know I'm doing something wrong but I can't see it.</p>

<p>My connections are </p>

<pre><code>SCLK --&gt; Arduino Pin 13
MISO --&gt; Arduino Pin 12
MOSI --&gt; Arduino Pin 11
Reset --&gt; Arduino Pin 10

VIN --&gt; 5V
GND --&gt; GND
</code></pre>

<p>I'm using a true Arduino UNO as the ISP. I've uploaded the ArduinoISP code into it, choose Arduino as ISP as Programmer and Arduino Uno on boards. The programming connections are just wired from Arduino UNO pins to some vias I've purposely added on the layout.</p>

<p>As mentioned in the comments, I'm adding an image of the layout here.  </p>

<p><a href="https://i.stack.imgur.com/7kEI2.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/7kEI2.png" alt="enter image description here"></a></p>

<p>I've tried this very circuit on an atmega328P soldered in a TQFP adapter and with the other components soldered on the adapter as well (looks like a jungle of wires) and somehow I was able to burn the bootloader. </p>

<p>Hoping someone can point out what's wrong.</p>
 35097: <p>It seems that you are using a lm317 voltage regulator to power your atmega328p MCU but I think you forgot the part that lm317 needs feedback of 1.25v with voltage divider network to set its variable output voltage in the schematic you have connected adj pin of  lm317 directly to GND.
S0 check your output vtg from your regulator and another issue voltage regulator only works great when difference between regulating voltage is lower then the supply voltage. </p>
