How to bridge between two computers

I have 3 machines connected like this:

Computer1 <----> Computer with Ubuntu 12.04 <-----> Computer2

(The Ubuntu computer has 2 ethernet interfaces.)

Computer1's IP address is 192.168.10.1, and Computer2's is 192.168.10.10.

I want to create a bridge in Ubuntu so Computer1 and Computer2 can talk to each other.

I created the bridge with

sudo ifconfig eth0 0.0.0.0 downsudo ifconfig eth1 0.0.0.0 downsudo brctl addbr br0sudo brctl addif br0 eth0sudo brctl addif br0 eth1sudo ifconfig br0 upsudo ifconfig eth0 promisc upsudo ifconfig eth1 promisc up

The command brctl showstp br0 shows me that the state of eth0 and eth1 is forwarding.

If I use Computer2 to ping Computer1, tshark sees this:

ARP 60 Who has 192.168.10.1? Tell 192.168.10.10

But I don't see ARP reply from Computer1.

However, tshark running at Computer1 says it did send a response:

ARP 60 Who has 192.168.10.1? Tell 192.168.10.10ARP 42 192.168.10.1 is at XX:XX:XX:XX:XX:XX (mac hidden)

So why isn't the ARP response going through the bridge, and how do I fix it?